Magnetic Fields - AP Physics C Electricity and Magnetism
A long, thin bar magnet with a north pole at one end and a south pole at the other is carefully broken exactly in the middle. Which of the following describes the result?
Answer: Two shorter, but complete, bar magnets are formed, each with its own north and south pole.
The correct answer is B. A direct consequence of the non-existence of magnetic monopoles is that if a magnet is broken, each piece will become a smaller magnet with both a north and a south pole. Magnetic field lines must form closed loops. A describes the creation of monopoles, which is not possible. C is incorrect because while a severe shock can demagnetize a material, breaking it does not automatically do so; the domain alignment largely persists. D is incorrect; both resulting pieces will be magnets.
A small magnetic compass is placed at a point in space. The direction that the north-seeking pole of the compass needle points indicates which of the following?
Answer: The direction of the magnetic field vector at that point.
The correct answer is A. By definition, the direction of the magnetic field vector B at any point is the direction that the north pole of a compass needle would point if placed at that point. C is equivalent to A, but A is the more formal definition of the field vector's direction. B and D relate to the electric field, not the magnetic field.
A magnetic compass needle is a small permanent magnet. When used on Earth's surface away from other magnets, its north-seeking pole points towards Earth's geographic North Pole. What can be directly inferred from this observation?
Answer: The Earth's magnetic pole located near the geographic North Pole has the polarity of a magnetic south pole.
The correct answer is A. The north pole of a magnet (like a compass needle) is attracted to, and points toward, a magnetic south pole. Therefore, for the compass to point towards the geographic North, the Earth's magnetic pole in that vicinity must be a magnetic south pole. B is a common misconception. C is incorrect, as the Earth's magnetic field has a vertical component except at the magnetic equator. D is incorrect; the Earth's core is too hot to be a permanent ferromagnet; the field is generated by electric currents in the molten outer core.
When a diamagnetic material is brought near the north pole of a strong magnet, it experiences a weak repulsive force. This repulsion occurs because the external magnetic field:
Answer: induces atomic magnetic moments in the material that are aligned in the opposite direction to the external field.
The correct answer is A. Diamagnetism is a property of all materials where an external magnetic field induces a weak magnetic dipole moment in the atoms that opposes the external field. This induced opposing field leads to a weak repulsive force. B is incorrect because the effect is induced and not permanent, and it's not an alignment of pre-existing moments. C incorrectly mixes electric and magnetic concepts. D is incorrect; the material does not affect the strong magnet's polarity.
At the microscopic level, the primary origin of magnetism in most materials is the result of which of the following?
Answer: The intrinsic magnetic dipole moment of electrons (spin) and their orbital motion around the nucleus.
The correct answer is B. The magnetic properties of materials are fundamentally due to the magnetic dipole moments created by electrons. These moments arise from two sources: the intrinsic angular momentum of the electron, known as spin, and the orbital angular momentum of the electron as it moves around the nucleus. A describes electric phenomena. C is incorrect because nuclear magnetic moments are much weaker and contribute negligibly to the overall magnetic properties of most materials. D is incorrect as the forces governing electron orbits are electrostatic, not gravitational.
Two bar magnets are held near each other. A repulsive force is observed between them. This observation implies that:
Answer: the north pole of one magnet is near the north pole of the other.
The correct answer is B. The fundamental rule of magnetic interaction is that like poles repel each other (north-north or south-south) and opposite poles attract each other (north-south). A repulsive force indicates that two like poles are near each other. A would result in an attractive force. C describes an orientation that would primarily result in torque. D does not determine the nature of the force, only the properties of the magnets.
What is a key difference between the properties of static electric field lines and magnetic field lines?
Answer: Static electric field lines can originate or terminate on charges, whereas magnetic field lines always form closed loops.
The correct answer is B. This statement reflects the existence of electric monopoles (charges) and the non-existence of magnetic monopoles. Electric field lines start on positive charges and end on negative charges. Magnetic field lines have no beginning or end; they are always continuous loops. A has the relationship reversed. C is incorrect; superposition applies to both electric and magnetic fields. D is partially incorrect; electric fields exert forces on both stationary and moving charges.
An initially unmagnetized sample of a material is placed in a strong external magnetic field. The sample becomes strongly magnetized and retains a significant amount of its magnetism after the external field is removed. This material is best classified as:
Answer: Ferromagnetic, because its magnetic domains align with the field and remain aligned due to hysteresis.
The correct answer is A. The ability to become strongly magnetized and retain that magnetism (remanence) is the defining characteristic of a ferromagnetic material. This is due to the alignment of large-scale magnetic domains. B is incorrect; paramagnetic materials are weakly attracted but do not retain magnetism. C is incorrect; diamagnetic materials are weakly repelled and the effect is induced, not permanent. D is incorrect; conductors can trap fields, but this is not the typical classification described.
Which of the following statements correctly describes the magnetic field lines produced by a permanent bar magnet?
Answer: They form closed loops which, by convention, emerge from the north pole and enter the south pole outside the magnet.
The correct answer is B. A fundamental property of magnetism is that magnetic field lines always form closed loops. They do not have a starting or ending point. By convention, the direction of the field outside the magnet is from the north pole to the south pole, and inside it is from south to north to complete the loop. A is incorrect because the lines do not terminate. C gives an inaccurate description of the field's geometry. D is incorrect; field lines show the direction of force on a magnetic north pole, not the path of a moving charge, whose path also depends on its velocity.
What is the key distinction between a 'hard' ferromagnetic material (used for permanent magnets) and a 'soft' ferromagnetic material (used for electromagnet cores)?
Answer: Hard materials retain their magnetism after an external field is removed, while soft materials do not.
The correct answer is B. The terms 'hard' and 'soft' in magnetism refer to a material's ability to retain magnetization. Hard materials have high coercivity and remanence, making them difficult to magnetize but also difficult to demagnetize, hence suitable for permanent magnets. Soft materials are easily magnetized and demagnetized, making them ideal for applications where the field needs to be switched, like in electromagnets. A and C are not the defining magnetic differences. D is incorrect as both types usually need to be magnetized initially.
In a diagram representing a magnetic field with field lines, what physical quantity corresponds to the density of the lines (how close they are to each other) in a given region?
Answer: The relative magnitude of the magnetic field strength in that region.
The correct answer is D. In any field line representation (electric or magnetic), the density of the lines is used to represent the magnitude, or strength, of the field. Where the lines are closer together, the field is stronger. A, B, and C are incorrect interpretations of a field line diagram.
The magnetic field produced by a magnetic dipole (like a small bar magnet) decreases with distance r from its center. For distances large compared to the dipole's size, the magnitude of the field B is proportional to:
Answer: 1/r3, due to the partial cancellation of north and south pole fields.
The correct answer is A. The field of a dipole is the superposition of the fields from a north and a south pole separated by a small distance. At large distances, these two fields nearly cancel, and the remaining field decreases much faster than that of a single pole. The resulting field magnitude is proportional to 1/r3. B describes the field of a monopole (which don't exist for magnetism). C describes the field of an infinitely long line of current. D is incorrect.
The Earth's magnetic field resembles that of a bar magnet. If a compass is used near the Earth's geographic South Pole, the north-seeking pole of the compass needle will primarily point:
Answer: upwards, away from the surface of the Earth.
The correct answer is C. The Earth's magnetic pole near the geographic South Pole is a magnetic north pole. Magnetic field lines emerge from a north pole. Therefore, near this pole, the field lines are directed predominantly away from the Earth's surface. The north-seeking pole of a compass aligns with these field lines and will point generally upwards. A and B describe horizontal alignment, which occurs closer to the magnetic equator. D would be the case near the magnetic south pole (near the geographic North Pole).
A sample of paramagnetic material, such as aluminum, is placed in a non-uniform magnetic field. The sample will experience a net force that is:
Answer: directed toward the stronger region of the field, because its permanent atomic dipoles partially align with the field.
The correct answer is B. Paramagnetic materials have permanent atomic magnetic dipoles that are randomly oriented. An external field causes them to partially align with the field, resulting in a net magnetic moment in the direction of the field. This causes the material to be weakly attracted to the magnet, and thus it will be pulled toward the region where the field is strongest. A describes the behavior of a diamagnetic material. C and D are incorrect descriptions of the net force.
The mathematical statement ∮B⋅dA=0 is known as Gauss's law for magnetism. What is the fundamental physical principle that this law represents?
Answer: The net magnetic flux through any closed surface is zero because magnetic monopoles have never been observed.
The correct answer is A. Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. This is a mathematical expression of the experimental observation that there are no magnetic monopoles (isolated north or south poles). Magnetic field lines always form closed loops, so any line entering a closed surface must also exit it. B is incorrect because the magnetic field is not conservative. C describes Ampère's Law, not Gauss's law for magnetism. D describes the magnetic Lorentz force, which is a different concept.
An unmagnetized iron rod becomes a temporary magnet when one end is brought near the north pole of a permanent magnet. This phenomenon of induced magnetism in the iron rod is best explained by the:
Answer: alignment of pre-existing, microscopic magnetic domains within the iron by the external magnetic field.
The correct answer is C. Iron is a ferromagnetic material, which contains small regions called magnetic domains where the atomic magnetic moments are already aligned. In an unmagnetized state, these domains are randomly oriented. An external magnetic field exerts a torque on these domains, causing them to align with the external field, thus magnetizing the rod. A describes electric polarization. B is incorrect as monopoles do not exist. D is incorrect as there is no significant transfer of charge.
Which of the following is an intrinsic property of the magnetic field vector B at a specific point in empty space?
Answer: A defined magnitude and direction, regardless of whether any object is present to experience its effects.
The correct answer is C. A field, by its nature, is a property of space itself, created by sources elsewhere. At any given point, the field has a specific vector value (magnitude and direction) whether or not there is a charge or magnet there to interact with it. A, B describe the effects of the field on an object, not the field itself; the force on a charge also depends on its velocity. D is incorrect; a field can exist in a vacuum, far from its sources.
Gauss's law for magnetism is one of the four fundamental Maxwell's equations. Its mathematical form, ∮B⋅dA=0, expresses a key property of magnetic fields. Which of the following is the most direct physical consequence described by this equation?
Answer: The non-existence of magnetic monopoles.
The correct answer is B. The equation states that the net magnetic flux out of any closed surface is zero. This implies there are no 'sources' or 'sinks' of magnetic field, which are hypothetical particles called magnetic monopoles. A is Faraday's law of induction. C is Ampère's law. D describes a property of electric fields, related to Gauss's law for electricity.
An imaginary closed spherical surface completely encloses the north pole of a bar magnet while the south pole is outside the surface. What is the net magnetic flux through the spherical surface?
Answer: Zero, because all magnetic field lines that exit the surface from the north pole must re-enter it to reach the south pole.
The correct answer is C. According to Gauss's law for magnetism, the net magnetic flux through any closed surface is always zero. This is because magnetic field lines are continuous loops without beginning or end. Even though the north pole is inside, the field lines that emerge from it and exit the surface must loop around and re-enter the surface somewhere else to continue towards the south pole. The total exiting flux is exactly canceled by the total entering flux. A and B would be true for electric flux and charges, but not for magnetic flux. D is incorrect because the result is always zero.
The magnetic permeability of a material, μ, relates the magnetic field strength inside the material to the external magnetic field. For a paramagnetic substance, the value of μ is:
Answer: slightly greater than the permeability of free space, μ0, indicating weak enhancement of the field.
The correct answer is C. Paramagnetic materials are weakly attracted to magnetic fields, meaning they slightly enhance the field within them. This corresponds to a magnetic permeability μ that is slightly larger than μ0. A is incorrect. B describes a diamagnetic material. D describes a ferromagnetic material.
