Magnetism and Moving Charges - AP Physics 2

1. A particle with charge $+1.0\,\mu\text{C}$ moves east at $6.0\times10^{4}\,\text{m/s}$ in a uniform magnetic field of $0.80\,\text{T}$ directed east. Which statement best describes the magnetic force on the particle?
   Answer: The force is zero. This problem tests understanding of magnetism and moving charges. The magnetic force on a charged particle follows F = qv × B, where the force is perpendicular to both velocity and field. When velocity and magnetic field are parallel (both pointing east), the cross product v × B equals zero, resulting in zero magnetic force. This occurs because sin(0°) = 0 in the force equation F = qvB sin(θ). Choice D incorrectly attributes zero force to the particle's motion, when actually it's due to the parallel alignment of v and B. Remember that magnetic force is maximum when v ⊥ B and zero when v ∥ B, regardless of charge magnitude or speed.
2. A stationary electron ($q=-e$) is placed in a uniform magnetic field of magnitude $0.70\,\text{T}$ directed upward. No electric field is present. Which statement best describes the magnetic force on the electron?
   Answer: It is zero because the electron's velocity is zero. This question tests understanding of magnetism and moving charges. The magnetic force is F = qv × B, which depends on the particle having a velocity. For a stationary particle (v = 0), the force is exactly zero regardless of the charge magnitude or the magnetic field strength. This is a fundamental property: magnetic fields only exert forces on moving charges. Choice D incorrectly assumes the force aligns with the field direction, missing that even if the electron were moving, the force would be perpendicular to B. Remember that magnetic force requires motion—no velocity means no magnetic force, period.
3. A proton moves upward at $9.0\times10^{5}\,\text{m/s}$ through a uniform magnetic field of $0.15\,\text{T}$ directed north. Which statement best describes the magnetic force on the proton?
   Answer: The force is westward. This problem tests understanding of magnetism and moving charges. The magnetic force on a charged particle is perpendicular to both its velocity and the magnetic field, calculated using F = qv × B. Applying the right-hand rule: point fingers upward (velocity), curl them north (field), and your thumb points west for a positive charge. Since a proton has positive charge, the force is westward. Choice D incorrectly suggests that upward motion prevents magnetic force, when actually force exists for any motion not parallel to the field. To solve these problems systematically, use the right-hand rule for the cross product, keeping the result for positive charges.
4. A positron ($q=+1.60\times10^{-19}\,\text{C}$) moves north at $1.5\times10^{7}\,\text{m/s}$ through a uniform magnetic field of $0.10\,\text{T}$ directed upward. Which statement best describes the magnetic force on the positron?
   Answer: The force is eastward. This problem tests understanding of magnetism and moving charges. The magnetic force is perpendicular to both the velocity and magnetic field vectors, calculated using F = qv × B. Using the right-hand rule: point fingers north (velocity), curl them upward (field), and your thumb points east for a positive charge. Since a positron has positive charge like a proton, the force is eastward. Choice D incorrectly assumes that any moving charged particle experiences no force, confusing this with the condition that only parallel motion to the field produces zero force. To solve these problems, systematically apply the right-hand rule for positive charges, keeping the same direction for positrons.
5. A proton ($q=+1.60\times10^{-19}\,\text{C}$) moves east at $3.0\times10^{6}\,\text{m/s}$ through a uniform magnetic field of $0.40\,\text{T}$ directed north. Which statement best describes the magnetic force on the proton?
   Answer: The force is upward. This problem tests understanding of magnetism and moving charges. The magnetic force on a moving charged particle is given by F = qv × B, where the force is perpendicular to both the velocity and magnetic field vectors. Using the right-hand rule: point your fingers east (velocity direction), curl them north (field direction), and your thumb points upward for a positive charge. Since the proton has positive charge, the force is indeed upward. Choice D incorrectly assumes that moving charges experience no magnetic force, confusing this with the fact that stationary charges experience no magnetic force. To solve these problems systematically, use the right-hand rule for positive charges, then reverse the direction for negative charges.
6. A particle with charge $q=+2.0\,\mu\text{C}$ moves west at $500\,\text{m/s}$ through a uniform magnetic field $\vec B=0.20\,\text{T}$ directed south. Which statement best describes the direction of the magnetic force on the particle?
   Answer: The force is directed downward. This problem tests magnetism and moving charges. The magnetic force F = qv × B acts perpendicular to both the velocity and magnetic field vectors. Using the right-hand rule: point fingers west (velocity), curl them south (field), and the thumb points downward for a positive charge. Since the particle has positive charge, the force is directed downward. Choice D shows the misconception that uniform fields produce no force, when actually the uniformity of the field doesn't affect whether force exists. To solve magnetic force problems, always use the right-hand rule systematically: fingers along velocity, curl toward field, thumb shows force direction for positive charges.
7. A particle with charge $q=+2.0\times10^{-6}\,\text{C}$ moves upward through a uniform magnetic field directed out of the page. No electric field is present. Which statement best describes the direction of the magnetic force on the particle?
   Answer: To the right. This question tests understanding of magnetism and moving charges. The magnetic force F = qv × B is perpendicular to both velocity and magnetic field vectors. With the particle moving upward and field pointing out of the page, apply the right-hand rule: fingers up (velocity), curl out of page (field), thumb points right. Since this is a positive charge, the force points to the right as the right-hand rule indicates. Choice D incorrectly assumes the force is zero because the field is perpendicular to the page, when actually perpendicular arrangements produce maximum force. Visualize the 3D geometry carefully and apply the right-hand rule systematically for these problems.
8. An electron ($q=-1.60\times10^{-19}\,\text{C}$) travels upward at $2.5\times10^{6}\,\text{m/s}$ through a uniform magnetic field $B=0.30\,\text{T}$ directed to the right. No electric field acts. Which statement best describes the direction of the magnetic force on the electron?
   Answer: Out of the page. This question tests understanding of magnetism and moving charges. The magnetic force on a moving charge is F = qv × B, which must be perpendicular to both the velocity and magnetic field vectors. For the electron moving upward with the field pointing right, we first apply the right-hand rule: fingers point up (velocity), curl right (field), giving thumb pointing out of the page. However, since the electron has negative charge, we must reverse this direction, so the force points out of the page. Choice D incorrectly claims that negative charges feel no magnetic force, when in fact they experience force in the opposite direction to positive charges. Always remember to apply the right-hand rule first, then flip the direction for negative charges.
9. A proton ($q=+1.60\times10^{-19}\ \text{C}$) enters a region of uniform magnetic field $\vec{B}=0.50\ \text{T}$ directed east. The proton's velocity is $3.0\times10^{6}\ \text{m/s}$ directed north. No electric fields are present. Which statement best describes the magnetic force on the proton?
   Answer: It is directed downward. This question tests magnetism and moving charges. The magnetic force on a moving charged particle is given by F = qv × B, where the force is perpendicular to both the velocity and magnetic field vectors. For a positive charge moving north with field pointing east, using the right-hand rule: point fingers north (velocity), curl them east (field), and thumb points down. The force is therefore directed downward. Choice C incorrectly assumes force is parallel to velocity, reflecting the misconception that forces always act in the direction of motion. Always use the right-hand rule for positive charges, remembering that magnetic force is perpendicular to both v and B.
10. A $+4.0\,\mu\text{C}$ particle is momentarily at rest in a uniform magnetic field of $0.70\,\text{T}$ directed downward. Which statement best describes the magnetic force on the particle?
    Answer: It is zero because the particle is not moving. This question tests understanding of magnetism and moving charges. The magnetic force is given by F = qv × B, where v is the particle's velocity. When a particle is at rest, its velocity v = 0, making the entire force expression equal to zero regardless of charge magnitude or field strength. This is fundamentally different from electric forces, which act on stationary charges. Choice D suggests there's always a perpendicular force, missing that velocity is required for magnetic force to exist. Remember that magnetic forces only act on moving charges; stationary charges experience no magnetic force even in the strongest fields.
11. A proton ($q=+e$) moves with speed $v=2.0\times10^{6}\,\text{m/s}$ through a uniform magnetic field of magnitude $B=0.60\,\text{T}$. The velocity is parallel to the field direction. No electric field is present. Which statement best describes the magnetic force on the proton?
    Answer: It is zero because $\vec v$ is parallel to $\vec B$. This question tests understanding of magnetism and moving charges. The magnetic force is given by F = qvB sin(θ), where θ is the angle between velocity and magnetic field vectors. When the velocity is parallel to the magnetic field (θ = 0°), sin(0°) = 0, making the entire force zero regardless of the charge's magnitude or sign. This occurs because the cross product v × B equals zero when vectors are parallel. Choice D incorrectly claims only electrons experience magnetic force, when actually all moving charges do—except when moving parallel to the field. To determine magnetic force, always check the angle between v and B first; if parallel, the force is automatically zero.
12. A particle with charge $q=-2.0\times10^{-6}\,\text{C}$ moves to the right at $v=400\,\text{m/s}$ through a uniform magnetic field $B=0.20\,\text{T}$ directed upward. No electric field acts. Which statement best describes the direction of the magnetic force on the particle?
    Answer: Into the page. This question tests understanding of magnetism and moving charges. The magnetic force F = qv × B must be perpendicular to both velocity and magnetic field vectors. For a particle moving right with field pointing upward, the right-hand rule gives: fingers right (velocity), curl upward (field), thumb points out of the page. However, this particle has negative charge, so we reverse the direction—the force points into the page. Choice C incorrectly assumes the force is parallel to velocity, when magnetic forces are always perpendicular to the motion. Remember to always check the sign of the charge and reverse the right-hand rule result for negative charges.
13. An electron moves east at $4.0\times10^{6}\,\text{m/s}$ through a uniform magnetic field of $0.50\,\text{T}$ directed upward. Which statement best describes the direction of the magnetic force on the electron?
    Answer: The force is directed south. This problem tests magnetism and moving charges. The magnetic force on a moving charge is F = qv × B, perpendicular to both velocity and field vectors. Applying the right-hand rule: fingers point east (velocity), curl upward (field), giving thumb pointing north for a positive charge. Since this is an electron (negative charge), we reverse the direction, making the force point south. Choice D incorrectly states there's no force when v ⊥ B, which is actually when magnetic force is maximum. For any magnetic force problem, use the right-hand rule first, then remember to reverse the direction for negative charges like electrons.
14. A $-1.5\,\mu\text{C}$ particle moves north at $4.0\times10^6\,\text{m/s}$ through a uniform magnetic field of $0.20\,\text{T}$ directed downward. Which statement best describes the magnetic force on the particle?
    Answer: It is directed east. This question tests understanding of magnetism and moving charges. The magnetic force F = qv × B acts perpendicular to both the particle's velocity and the magnetic field direction. Using the right-hand rule: fingers point north (velocity), curl downward (field direction), thumb points west for a positive charge. Since this particle has negative charge (-1.5 μC), we reverse the direction, making the force point east. Choice D incorrectly suggests uniform fields produce no force, confusing field uniformity with the perpendicular relationship between v and B that determines force. Always apply the right-hand rule for positive charges first, then reverse for negative charges.
15. An alpha particle ($q=+3.2\times10^{-19}\ \text{C}$) moves due north at $2.5\times10^{6}\ \text{m/s}$ through a uniform magnetic field of magnitude $0.20\ \text{T}$ directed downward. No electric fields are present. Which statement best describes the direction of the magnetic force on the alpha particle?
    Answer: It is directed west. This question tests magnetism and moving charges. The magnetic force direction is determined by F = qv × B, perpendicular to both velocity and field vectors. For positive charge moving north with field downward, apply right-hand rule: fingers north (velocity), curl down (field), thumb points west. The force is therefore directed west. Choice C incorrectly assumes force parallels the magnetic field, violating the fundamental perpendicularity of magnetic forces. Always verify your right-hand rule by checking that F ⊥ v and F ⊥ B.
16. An electron ($q=-1.60\times10^{-19}\ \text{C}$) moves at $2.0\times10^{6}\ \text{m/s}$ due east through a uniform magnetic field of magnitude $0.40\ \text{T}$ directed upward. No electric fields are present. Which statement best describes the direction of the magnetic force on the electron?
    Answer: It is directed south. This question tests magnetism and moving charges. The magnetic force F = qv × B is perpendicular to both velocity and magnetic field, with direction determined by the cross product. For the electron moving east with field upward, the right-hand rule gives force pointing north, but since the electron is negative, we reverse this to get south. The magnitude is |F| = |q|vB sin(90°) = 1.28 × $10^{-13}$ N. Choice C incorrectly suggests force is parallel to velocity, a common misconception from everyday experience with contact forces. For negative charges, apply the right-hand rule then reverse the direction.
17. A particle with charge $+4.0\,\mu\text{C}$ moves north at $3.0\times10^{4}\,\text{m/s}$ through a uniform magnetic field of $0.40\,\text{T}$ directed east. Which statement best describes the magnetic force on the particle?
    Answer: The force is downward. This problem tests understanding of magnetism and moving charges. The magnetic force is perpendicular to both velocity and magnetic field, following F = qv × B. Using the right-hand rule: point fingers north (velocity), curl them east (field), and your thumb points downward for a positive charge. Since the particle has positive charge (+4.0μC), the force is downward as calculated. Choice D shows the misconception that moving particles experience no magnetic force, when actually only particles at rest or moving parallel to B experience zero force. Remember to apply the right-hand rule systematically: fingers along v, curl toward B, thumb shows F for positive charges.
18. An electron moves north at $8.0\times10^{6}\,\text{m/s}$ through a uniform magnetic field of $0.25\,\text{T}$ directed west. Which statement best describes the magnetic force on the electron?
    Answer: The force is upward. This problem tests understanding of magnetism and moving charges. The magnetic force on a moving charge is perpendicular to both velocity and magnetic field, following F = qv × B. Using the right-hand rule: point fingers north (velocity), curl them west (field), and your thumb points downward for a positive charge. Since this is an electron with negative charge, we reverse the direction, making the force upward. Choice D shows the misconception that electrons in motion experience no force, when actually all moving charges experience magnetic force unless v is parallel to B. To solve magnetic force problems, apply the right-hand rule consistently, then reverse the result for negative charges.
19. A particle with charge $q=-2.0\times10^{-6}\ \text{C}$ moves at $1.5\times10^{3}\ \text{m/s}$ due north through a uniform magnetic field $\vec{B}=0.20\ \text{T}$ directed due north. No electric fields are present. Which statement best describes the magnetic force on the particle?
    Answer: It is zero because $\vec{v}$ is parallel to $\vec{B}$. This question tests magnetism and moving charges. The magnetic force F = qv × B depends on the cross product of velocity and magnetic field vectors. When velocity and magnetic field are parallel (both pointing north), their cross product is zero, resulting in zero magnetic force regardless of charge magnitude or sign. This is because sin(0°) = 0 in the formula F = |q|vB sin(θ). Choice D incorrectly suggests force should be parallel to velocity, missing that magnetic forces are always perpendicular. Remember that parallel velocity and field vectors always produce zero magnetic force.
20. A proton ($q=+1.60\times10^{-19}\ \text{C}$) moves due east at $5.0\times10^{6}\ \text{m/s}$ through a uniform magnetic field of magnitude $0.30\ \text{T}$ directed due north. No electric fields are present. Which statement best describes the direction of the magnetic force on the proton?
    Answer: It is directed upward. This question tests magnetism and moving charges. The magnetic force direction is found using F = qv × B, where the cross product determines perpendicularity. For a proton moving east with field pointing north, apply the right-hand rule: fingers east (velocity), curl north (field), thumb points up. Since the proton is positive, the force is upward. Choice C incorrectly assumes force acts along velocity direction, a misconception from everyday pushing/pulling experiences. Use the right-hand rule systematically: fingers along v, curl toward B, thumb shows F for positive charges.

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