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 (-i), 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

Explanation:

To solve this, we analyze each option based on Faraday's Law (induced current depends on relative motion and magnetic polarity) and Lenz's Law (direction of induced current opposes the change in flux):

Option 1: Stationary magnet, coil rotating at 20 cm/s

Rotation of the coil does not create the same relative motion (toward the magnet) as the original scenario (magnet moving toward stationary coil). The flux change will differ, so induced current/direction won’t match. Eliminated.

Option 2: Both moving toward each other at 10 cm/s each

Relative speed = \( 10 + 10 = 20 \, \text{cm/s} \) (same as original relative speed: \( 20 + 0 = 20 \, \text{cm/s} \)). Polarity is normal (same as original), so flux change rate and direction (due to relative motion) match. Induced current magnitude and direction will be the same. Valid.

Option 3: Reversed polarity magnet moving at 10 cm/s toward coil

Original relative speed: \( 20 \, \text{cm/s} \); here, relative speed is \( 10 \, \text{cm/s} \) (slower). Also, reversed polarity changes the flux direction, so induced current direction will reverse (or magnitude differ). Eliminated.

Option 4: Normal polarity magnet stationary, coil approaching at 15 cm/s

Relative speed = \( 15 \, \text{cm/s} \) (less than original \( 20 \, \text{cm/s} \)), so flux change rate is lower. Induced current magnitude will be smaller. Eliminated.

Option 5: Reversed polarity magnet moving away at 20 cm/s

• Original: Normal magnet moves toward coil (flux increases, induced current opposes: direction = \(-I\)).
• Here: Reversed magnet moves away (flux decreases, but reversed polarity means the “opposing” current direction (via Lenz) will match \(-I\)).
• Relative speed: \( 20 \, \text{cm/s} \) (same magnitude as original). Flux change rate (magnitude) matches, and direction of current matches \(-I\) (due to reversed polarity + opposite motion). Valid.

Answer:

• 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