Question

A normal polarity magnet moves toward a stationary coil at 20 cm/s, and induces a maximum current of –8 mA. Which scenarios would induce the same maximum current and the same current direction (–), if the distance between the two objects is the same? Check all that apply.

a stationary magnet and a coil rotating at 20 cm/s rather than moving
both the magnet and the coil moving toward each other at 10 cm/s each
a reversed polarity magnet moving toward a stationary coil at 10 cm/s
a normal polarity magnet stationary with a coil approaching at 15 cm/s
a reversed polarity magnet moving away from the coil at 20 cm/s

Answer 1

Correct choices:
- both the magnet and the coil moving toward each other at 10 cm/s each
- a reversed polarity magnet moving away from the coil at 20 cm/s

Why:
- The induced emf (and current magnitude) depends on the rate of change of magnetic flux, i.e. on the relative speed along the approach axis. Two objects moving toward each other at 10 cm/s each have a closing speed of 20 cm/s, so the flux change rate (and magnitude of current) is the same, and the approach direction is the same so the current sign is the same.
- Reversing the magnet polarity flips the sign of the flux but reversing the motion (toward → away) also flips the sign of dΦ/dt; the two sign flips cancel, so a reversed magnet moving away at the same speed produces the same magnitude and same sign of induced current.

Why the others fail:
- Rotating the coil does not produce the same axial flux change as translating it toward the magnet (generally not equivalent).
- Reversed polarity moving toward at 10 cm/s both changes the sign and reduces the speed, so magnitude and sign differ.
- Approaching at 15 cm/s gives a smaller flux-change rate, so the current magnitude is different.