If there is no relative motion between a charge and a magnetic field, the magnetic force on the charge is zero.

If there is no relative motion between a charge and a magnetic field, the magnetic force on the charge is zero.

• A. True
• B. False
• C. Sometimes
• D. Always

Answer: (A)

Magnetic force on a charge depends on the charge’s velocity relative to the magnetic field, via F = q v × B. If the charge is at rest with respect to the field (v = 0), the cross product is zero and there is no magnetic force. Magnetic fields don’t do work on stationary charges; they only exert force when the charge is moving. If the magnetic field changes with time, an electric field is induced and that can push the charge, but that’s an electric, not a magnetic, effect. So in a static magnetic field with no motion, the magnetic force is zero, which makes the statement true. If the charge moves, the force appears depending on the direction of motion relative to B.

Magnetic force on a charge depends on the charge’s velocity relative to the magnetic field, via F = q v × B. If the charge is at rest with respect to the field (v = 0), the cross product is zero and there is no magnetic force. Magnetic fields don’t do work on stationary charges; they only exert force when the charge is moving. If the magnetic field changes with time, an electric field is induced and that can push the charge, but that’s an electric, not a magnetic, effect. So in a static magnetic field with no motion, the magnetic force is zero, which makes the statement true. If the charge moves, the force appears depending on the direction of motion relative to B.