A 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 10⁴ turns.The current in the solenoid changes at a rate of 6.0 A/s.A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown.

-Determine the mutual inductance of this combination.

Question

A 0.100-m long solenoid has a radius of 0.050 m and 1.50 × 10⁴ turns.The current in the solenoid changes at a rate of 6.0 A/s.A conducting loop of radius 0.0200 m is placed at the center of the solenoid with its axis the same as that of the solenoid as shown.
 
-Determine the mutual inductance of this combination.

Quizplus · Accepted Answer

The mutual inductance of a solenoid and a loop is given by the equation M = μ₀n²πr²l, where n is the number of turns per unit length and l is the length of the solenoid. We can calculate n by dividing the total number of turns (1.5 × 10⁴) by the length of the solenoid (0.1 m). This gives us n = 1.5 × 10⁵ turns/m.

Using this value for n, along with the given radius and length of the solenoid, we find that the mutual inductance is:

M = (4π × 10⁻⁷ T·m/A) × (1.5 × 10⁵ turns/m)² × (0.05 m)² × (0.1 m)
M = 2.4 × 10⁻⁴ H

Therefore, the best choice is B.

A 0100-M Long Solenoid Has a Radius of 0