In a DC motor, a current-carrying coil sits in a magnetic field and experiences forces that make it rotate. Which energy transformation best describes what happens during steady operation (ignoring losses)?
Answer: Electrical energy supplied to the coil is transferred via magnetic forces into mechanical (rotational) energy of the motor.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Magnetic fields can do work on current-carrying coils—electrical energy supplied to the coil creates currents that interact with the magnetic field, producing forces that cause rotation, transferring energy to mechanical (rotational) energy without direct contact. In this scenario, the current in the coil interacts with the magnetic field to produce torque, converting input electrical power to output mechanical power during steady operation. Choice C is correct because it correctly identifies the energy conversion pathway from electrical to mechanical via magnetic forces in the motor. Choice A confuses the process with a generator, reversing the energy flow from mechanical to electrical. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A metal ring is placed near (but not touching) a solenoid. The current in the solenoid is rapidly increased, and the ring briefly experiences a force and moves. What best explains the energy transfer that causes the ring to move?
Answer: The solenoid's changing magnetic field induces a current in the ring; the induced current interacts with the magnetic field, transferring energy to the ring's kinetic energy.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electromagnetic induction allows energy transfer through changing magnetic fields—when current in a primary coil creates a changing magnetic field (by varying the current), this changing field passes through a nearby secondary coil inducing an EMF and current (Faraday's law), transferring electrical energy from primary to secondary without any direct electrical connection, with the field acting as the energy carrier. In this scenario, the rapidly increasing current in the solenoid creates a changing magnetic flux through the ring, inducing a current that interacts with the magnetic field to produce a force, transferring energy to the ring's kinetic energy across the gap. Choice A is correct because it accurately explains the induction mechanism and the role of the induced current in energy transfer via the magnetic field. Choice B incorrectly claims static fields do work on stationary charges, confusing magnetic force requirements. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A positively charged particle with q=+2.0×10−6C moves 0.50m through a uniform electric field E=4.0×103N/C. The displacement is directly opposite the direction of the electric field. How much work does the electric field do on the particle?
Answer: −4.0×10−3J
This question tests understanding of how electric fields transfer energy without requiring direct physical contact between objects. Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd cos θ, where θ is the angle between field and displacement; this converts field energy to kinetic energy of the charge even without direct contact. In this scenario, the positive charge q = +2.0×10⁻⁶ C moves d = 0.50 m opposite to the electric field E = 4.0×10³ N/C (θ = 180°), so the field does work W = qEd cos(180°) = (2.0×10⁻⁶ C)(4.0×10³ N/C)(0.50 m)(-1) = -4.0×10⁻³ J. The negative work means the field removes energy from the particle (slowing it down if initially moving). Choice B is correct because it accurately calculates work as -4.0×10⁻³ J, recognizing that work is negative when displacement opposes the force direction. Choice A incorrectly gives positive work, missing that motion opposite to field direction yields negative work; Choice C shows wrong magnitude; Choice D falsely claims electric fields cannot do work. The key insight is that fields can do positive or negative work depending on relative directions—positive work accelerates charges along field lines, negative work decelerates charges moving against field lines.
A transformer has a primary coil connected to an AC source and a secondary coil connected to a lamp. The coils are separated by an insulating core so there is no direct electrical connection between them. Which statement best describes how energy gets from the primary coil to the lamp?
Answer: Energy is transferred by the changing magnetic field produced by the primary, which induces an emf and current in the secondary.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electromagnetic induction allows energy transfer through changing magnetic fields—when current in a primary coil creates a changing magnetic field (by varying the current), this changing field passes through a nearby secondary coil inducing an EMF and current (Faraday's law), transferring electrical energy from primary to secondary without any direct electrical connection, with the field acting as the energy carrier. In this scenario, the changing current in the primary coil creates a changing magnetic flux through the secondary, inducing EMF which drives current to the lamp, delivering power to light it up, with the field serving as the intermediary across the insulating core. Choice B is correct because it accurately explains that the field acts as energy carrier allowing non-contact transfer and correctly identifies the energy conversion pathway through the changing magnetic field. Choice A incorrectly claims direct contact is required via electrons jumping, missing that fields transfer energy across gaps and confusing it with conduction. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A positive ion with charge q=2.0×10−6C moves in the direction of a uniform electric field E=5.0×103N/C through a distance d=0.50m. How much energy is transferred to the ion by the electric field (work done by the field)?
Answer: W=5.0×10−3J
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd, converting field energy to kinetic energy of the charge, and this occurs even though there's no direct contact between the source charges creating the field and the charge being accelerated. In this scenario, the electric field E = 5.0×103 N/C does work on charge q = 2.0×10−6 C as it moves distance d = 0.50 m, transferring energy W = qEd = (2.0×10−6)(5.0×103)(0.50) = 5.0×10−3 J from the field to the ion. Choice A is correct because it accurately calculates the work W = 5.0×10−3 J using W = qEd and recognizes the energy transfer to the ion. Choice B incorrectly halves the value, perhaps by misapplying the distance or overlooking the factor of 0.50. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A charged oil droplet with charge q=+1.0×10−9C moves upward d=0.10m in a uniform electric field of magnitude E=2.0×104N/C that points upward. Ignoring gravity and drag, which statement correctly describes the energy transfer and its amount?
Answer: The electric field does work W=qEd=2.0×10−6J on the droplet, increasing its kinetic energy.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd, converting field energy to kinetic energy of the charge, and this occurs even though there's no direct contact between the source charges creating the field and the charge being accelerated. In this scenario, the electric field E = 2.0×104 N/C does work on the droplet q = +1.0×10−9 C as it moves distance d = 0.10 m upward along the field, transferring energy W = qEd = (1.0×10−9)(2.0×104)(0.10) = 2.0×10−6 J from the field to the droplet's kinetic energy. The field serves as the intermediary, storing energy when created by the source and releasing it to the receiver without requiring physical contact. Choice A is correct because it accurately calculates and describes the work using W = qEd for the energy transfer. Choice B is incorrect because it uses an inverted formula W = E/(qd), leading to a wrong value and misunderstanding the work calculation. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A transformer operates with no direct electrical connection between its primary and secondary coils. If the primary delivers Pin=500W to the magnetic field in the core region and the transformer is 90% efficient, what is the best description of where the missing 10% of the power goes?
Answer: It is dissipated as thermal energy (and possibly sound) due to resistive losses and magnetic losses, even though energy transfer to the secondary occurs via the field.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electromagnetic induction allows energy transfer through changing magnetic fields—when current in a primary coil creates a changing magnetic field, this changing field passes through a nearby secondary coil inducing an EMF and current (Faraday's law), transferring electrical energy from primary to secondary without any direct electrical connection. In this scenario, the transformer receives Pin = 500 W at the primary, transfers 90% (450 W) to the secondary load via the magnetic field, and the missing 10% (50 W) must go somewhere due to energy conservation. The field serves as the intermediary for the 450 W transfer, but real transformers have losses. Choice D is correct because it accurately explains that the missing 50 W is dissipated as thermal energy due to resistive losses in windings (I²R heating) and magnetic losses in the core (hysteresis and eddy currents), even though the main energy transfer occurs via the field. Choice A violates energy conservation; Choice B incorrectly suggests energy remains trapped in the field; Choice C wrongly implies the secondary receives more than 100% power. Real transformers demonstrate both the power of field-based energy transfer and the practical limitations—while fields enable non-contact transfer, material properties cause unavoidable losses manifesting as heat.
A transformer has a primary coil connected to a 200 W AC source. The transformer transfers energy to a secondary coil with no direct electrical connection. If the efficiency is η=0.80, what is the power delivered to the load on the secondary side?
Answer: 160 W
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electromagnetic induction allows energy transfer through changing magnetic fields—when current in a primary coil creates a changing magnetic field (by varying the current), this changing field passes through a nearby secondary coil inducing an EMF and current (Faraday's law), transferring electrical energy from primary to secondary without any direct electrical connection, with the field acting as the energy carrier. In this scenario, the transformer uses changing magnetic fields to transfer energy from primary to secondary, and with efficiency η=0.80, the output power is P_out = η P_in = 0.80 × 200 W = 160 W delivered to the load. Choice A is correct because it properly identifies the energy transfer via induction and calculates output power accounting for efficiency. Choice B incorrectly ignores efficiency, using the full input power. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A charged oil droplet with charge q=1.0×10−9C moves d=0.10m through a uniform electric field E=4.0×104N/C. The droplet speeds up even though it does not touch the plates creating the field. Which best explains the energy transfer to the droplet?
Answer: The electric field does work on the charge, transferring energy to the droplet's kinetic energy without contact.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. For electric field: Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd, converting field energy to kinetic energy of the charge, and this occurs even though there's no direct contact between the source charges creating the field and the charge being accelerated. In this scenario, the electric field E = 4.0×104 N/C does work on charge q = 1.0×10−9 C as it moves distance d = 0.10 m, transferring energy W = qEd = 1.0×10−9 × 4.0×104 × 0.10 = 4.0×10−6 J from the field to the droplet's kinetic energy, explaining the speedup without touching the plates. Choice A is correct because it accurately explains that the field acts as energy carrier allowing non-contact transfer and correctly identifies the energy conversion pathway through the electric field. Choice C incorrectly describes the wrong field type (magnetic when electric), confusing energy forms and failing to recognize the electric field's role as intermediary. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A wireless charging pad contains a primary coil connected to a power source. An alternating current in the primary coil creates a changing magnetic field across a small air gap. A secondary coil inside a phone sits above the pad with no metal contacts between them, and the phone begins charging. Which statement best explains how energy is transferred from the pad to the phone?
Answer: A changing magnetic field produced by the primary coil induces an emf and current in the secondary coil, transferring energy through the electromagnetic field across the gap.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electromagnetic induction allows energy transfer through changing magnetic fields—when current in a primary coil creates a changing magnetic field (by varying the current), this changing field passes through a nearby secondary coil inducing an EMF and current (Faraday's law), transferring electrical energy from primary to secondary without any direct electrical connection, with the field acting as the energy carrier. In this scenario, the changing current in the primary coil creates a changing magnetic flux through the secondary, inducing EMF ε = -dΦ/dt which drives current in the secondary coil, delivering power to charge the phone across the air gap. Choice B is correct because it accurately explains that the changing magnetic field acts as energy carrier allowing non-contact transfer via induction. Choice A incorrectly claims direct electron flow through air is needed, missing that fields transfer energy across gaps without conduction. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A current-carrying wire in a uniform magnetic field experiences a force F=BIL (wire is perpendicular to B). In an experiment, B=0.50T, I=2.0A, and L=0.30m. The wire segment is free to slide and moves d=0.40m while the current is maintained. How much energy is transferred to the wire's motion by the magnetic force?
Answer: W=0.12J
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Magnetic fields can do work on current-carrying wires—when a wire with current I is in magnetic field B, the force F = BIL sinθ does work W = Fd as the wire moves distance d, converting electrical energy to mechanical energy, as in motors, without direct contact between the magnet and the wire. In this scenario, the magnetic field B = 0.50 T exerts force F = BIL = (0.50)(2.0)(0.30) = 0.30 N on the wire, and as it moves d = 0.40 m, the work done is W = Fd = 0.30 × 0.40 = 0.12 J, transferring energy to the wire's motion. Choice A is correct because it accurately calculates the work W = 0.12 J using W = BILd and recognizes the energy transfer by the magnetic force. Choice B incorrectly doubles the value, perhaps by miscalculating F as 0.75 N. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A small sphere with charge q=+3.0×10−6C is placed in a uniform electric field E=1.5×104N/C. It moves d=0.20m in the direction of the electric field lines. How much work does the electric field do on the sphere (i.e., how much energy is transferred to the sphere by the field)?
Answer: 9.0×10−3J
This question tests understanding of how electric fields transfer energy without requiring direct physical contact between objects. Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd, converting field energy to kinetic energy of the charge, and this occurs even though there's no direct contact between the source charges creating the field and the charge being accelerated. In this scenario, the electric field E = 1.5×10⁴ N/C does work on charge q = 3.0×10⁻⁶ C as it moves distance d = 0.20 m, transferring energy W = qEd = (3.0×10⁻⁶ C)(1.5×10⁴ N/C)(0.20 m) = 9.0×10⁻³ J from the field to the sphere's kinetic energy. The field serves as the intermediary, storing energy when created by the source and releasing it to the charged sphere across the gap. Choice A is correct because it accurately calculates work using W = qEd = 9.0×10⁻³ J. Choice B incorrectly calculates 2.25×10⁻² J (possibly multiplying by extra factor), Choice C gives 9.0×10⁻² J (order of magnitude error), and Choice D shows 1.0×10⁻¹⁰ J (completely wrong calculation). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion).
In a simple DC motor, a current-carrying coil sits in a magnetic field and experiences forces that make it rotate. There is no need for the magnet to touch the coil. Which energy transformation best describes what happens as the coil turns?
Answer: Electrical energy supplied to the coil is transferred through the magnetic field to mechanical energy of rotation.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. In a DC motor, magnetic forces on currents do work W = Fd with F = BIL, converting electrical energy to mechanical energy through the magnetic field's mediation. In this scenario, electrical energy supplied to the coil creates current I, which experiences force F = BIL in the magnetic field B, causing rotation; the magnetic field transfers energy from the electrical circuit to mechanical motion without any physical contact between magnet and coil. The field serves as the intermediary, storing energy density proportional to B² and releasing it as mechanical work on the current-carrying conductors. Choice B is correct because it accurately identifies the energy conversion pathway: electrical → magnetic field → mechanical rotation. Choice A incorrectly suggests thermal energy and contact forces are involved; Choice C wrongly invokes gravitational potential energy which is irrelevant in typical motor operation; Choice D reverses the energy flow direction and incorrectly states magnetic forces oppose motion (they actually drive the rotation in motors). Energy transfer via fields enables all electric motors—from tiny phone vibrators to massive industrial drives—demonstrating how fields serve as energy carriers between electrical sources and mechanical loads.
A straight conductor of length L=0.50m carries current I=2.0A in a uniform magnetic field B=0.20T oriented for maximum force. The wire is constrained so it does not move. Which statement about energy transfer by the magnetic field is correct in this situation?
Answer: The magnetic field can exert a force F=BIL, but with zero displacement the mechanical work done on the wire is W=0.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Magnetic fields can do work on current-carrying wires—when a wire with current I in magnetic field B moves through distance d, the field exerts force F = BIL and does work W = Fd, converting electrical energy to mechanical kinetic energy, and this occurs without direct contact between the magnet and the wire. In this scenario, the magnetic field B = 0.20 T exerts maximum force F = BIL = (0.20)(2.0)(0.50) = 0.20 N on the wire, but with zero displacement (d=0), the work done is W = Fd = 0 J. The field serves as the intermediary, but no energy is transferred mechanically without motion, even though a force is present. Choice B is correct because it recognizes that work requires displacement, so W=0 despite the force, correctly applying W=Fd. Choice C is incorrect because it assumes a force always implies work, ignoring the need for displacement in the work definition. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A straight wire segment of length L=0.30m carries a current I=4.0A while in a uniform magnetic field B=0.50T oriented so the magnetic force on the wire is maximum. The wire is free to move and is pushed a distance d=0.20m by the magnetic force (no direct contact with any pusher). Using F=BIL and W=Fd, how much work is done on the wire by the magnetic force?
Answer: 0.12J
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Magnetic fields can do work on current-carrying wires—when a wire with current I in magnetic field B moves through distance d, the field exerts force F = BIL and does work W = Fd, converting electrical energy to mechanical kinetic energy, and this occurs without direct contact between the magnet and the wire. In this scenario, the magnetic field B = 0.50 T exerts maximum force F = BIL = (0.50)(4.0)(0.30) = 0.60 N on the wire, doing work W = Fd = (0.60)(0.20) = 0.12 J as it moves d = 0.20 m. The field serves as the intermediary, storing energy when created by the source and releasing it to the receiver without requiring physical contact. Choice A is correct because it correctly calculates the work using W = BILd and recognizes the energy conversion pathway through the field. Choice C is incorrect because it makes a calculation error, likely misapplying the formula or units. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
A straight wire segment of length L=0.40m carries current I=5.0A through a region of uniform magnetic field B=0.60T, oriented so the magnetic force on the wire is maximized. The wire is free to move, and it is displaced by d=0.20m in the direction of the magnetic force. How much work is done on the wire by the magnetic force?
Answer: 0.24J
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), converting electrical energy to mechanical energy through the magnetic field's mediation. In this scenario, the magnetic force on the wire is F = BIL = (0.60 T)(5.0 A)(0.40 m) = 1.2 N, and as the wire moves distance d = 0.20 m in the direction of this force, the magnetic field does work W = Fd = (1.2 N)(0.20 m) = 0.24 J, transferring energy from the field to the wire's kinetic energy. The field serves as the intermediary, converting electrical energy (from the current source) into mechanical energy of the wire's motion. Choice A is correct because it accurately calculates work using W = Fd = BILd = 0.24 J. Choice B incorrectly calculates 2.4 J (order of magnitude error), Choice C gives 0.12 J (possibly using wrong length or distance), and Choice D shows 1.2 J (confusing force with work). Energy transfer via magnetic fields enables motors, generators, and electromagnetic actuators—the magnetic field acts as the energy carrier between electrical and mechanical systems without requiring direct mechanical linkages.
A student claims: "Energy can only be transferred if objects are in direct contact; fields can exert forces but cannot transfer energy." Which response best corrects the claim using a field-based example?
Answer: The claim is incorrect: for example, a changing magnetic field from a primary coil can induce current in a nearby secondary coil, transferring energy across an air gap.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electromagnetic induction allows energy transfer through changing magnetic fields—when current in a primary coil creates a changing magnetic field (by varying the current), this changing field passes through a nearby secondary coil inducing an EMF and current (Faraday's law), transferring electrical energy from primary to secondary without any direct electrical connection, with the field acting as the energy carrier. The student's claim that fields cannot transfer energy is fundamentally incorrect, as demonstrated by countless technologies from transformers to wireless chargers. Fields serve as the intermediary, storing energy when created and releasing it to receivers across gaps without any physical contact. Choice C is correct because it provides a clear counterexample: electromagnetic induction in transformers proves fields transfer energy across air gaps. Choice A incorrectly supports the false claim; Choice B wrongly suggests only magnetic fields transfer energy and invents "stored mechanical energy" in magnets; Choice D incorrectly attributes energy transfer to air molecules rather than fields. Energy transfer via fields is fundamental to modern technology: wireless charging, radio transmission, solar panels capturing electromagnetic radiation, and particle accelerators all demonstrate non-contact energy transfer through fields.
A current-carrying wire of length L=0.25m in a uniform magnetic field experiences a magnetic force of magnitude F=BIL. The wire is pushed by this force and moves d=0.40m. If B=0.80T and I=4.0A (with orientation for maximum force), how much energy is transferred to the wire's motion by the magnetic field (work done)?
Answer: 0.32J
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Magnetic forces on currents do work W = Fd with F = BIL, converting electrical energy to mechanical energy through the magnetic field's mediation. In this scenario, the magnetic force on the wire is F = BIL = (0.80 T)(4.0 A)(0.25 m) = 0.80 N, and as the wire moves distance d = 0.40 m in the direction of this force, the magnetic field does work W = Fd = (0.80 N)(0.40 m) = 0.32 J, transferring energy from the field to the wire's kinetic energy. The field serves as the intermediary, converting electrical energy (from the current source) into mechanical energy of the wire's motion without requiring direct contact. Choice B is correct because it accurately calculates work using W = Fd = 0.32 J. Choice A incorrectly gives 0.80 J (possibly confusing force magnitude with work), Choice C shows 3.2 J (order of magnitude error), and Choice D gives 0.20 N which is a force unit, not energy. Energy transfer via magnetic fields is the foundation of electric motors, speakers, and electromagnetic actuators—demonstrating how fields enable conversion between electrical and mechanical energy across air gaps.
An electron (q=−1.60×10−19C) is released from rest in a uniform electric field of magnitude E=3.0×104N/C directed to the right. It travels a distance d=0.20m before hitting a screen. Ignoring other forces, how much work does the electric field do on the electron (and thus how much kinetic energy does the electron gain)?
Answer: W=+9.6×10−16J
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd, converting field energy to kinetic energy of the charge, and this occurs even though there's no direct contact between the source charges creating the field and the charge being accelerated. In this scenario, the electric field E = 3.0×104 N/C does work on charge q = -1.60×10−19 C as it moves distance d = 0.20 m, transferring energy W = qEd = (−1.60×10−19)(3.0×104)(0.20) but considering directions, the magnitude is 9.6×10−16 J and positive since the field accelerates the electron, increasing its kinetic energy. Choice B is correct because it accurately calculates the positive work W = +9.6×10−16 J done by the field, reflecting the kinetic energy gain. Choice A incorrectly claims negative work and energy loss, missing that the field does positive work on the accelerating electron despite its negative charge. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
Two parallel metal plates create a uniform electric field between them. A small positively charged bead is released from rest and accelerates toward the negative plate without touching anything else. Which statement correctly identifies the mechanism and energy source for the bead's kinetic energy gain?
Answer: The bead gains kinetic energy because the electric field does work on it; the energy ultimately comes from the external source that separated charges to create the field.
This question tests understanding of how electric and magnetic fields transfer energy without requiring direct physical contact between objects. Electric fields can do work on charges and transfer energy—when a charge q moves through distance d in electric field E, the field does work W = qEd, converting field energy to kinetic energy of the charge, and this occurs even though there's no direct contact between the source charges creating the field and the charge being accelerated. In this scenario, the uniform electric field between the plates accelerates the positive bead toward the negative plate, doing work to increase its kinetic energy, with the energy sourced from the external work done to separate the charges on the plates. Choice A is correct because it accurately explains that the electric field acts as the intermediary for non-contact energy transfer from the source to the bead's kinetic energy. Choice B incorrectly claims direct contact forces through air, failing to identify the field's role. Energy transfer via fields: electric fields accelerate charges doing work W = qEd (field energy → kinetic energy), magnetic forces on currents do work W = Fd with F = BIL (electrical → mechanical in motors), changing magnetic fields induce currents transferring energy between circuits (Faraday's law: electromagnetic induction), and electromagnetic waves carry energy through space at light speed (radiation energy). The key insight is fields serve as energy carriers, storing energy when created and releasing it to objects within the field, enabling energy transfer without material contact—this is fundamentally different from conduction (needs contact) or convection (needs fluid motion), and explains wireless charging (induction), motors (magnetic force work), particle accelerators (electric field acceleration), and solar panels (EM wave absorption).
