Question

A square loop of side length \( a \) is moving away from an infinitely long current-carrying conductor at a constant speed \( v \) as shown. Let \( x \) be the instantaneous distance between the long conductor and side AB. The mutual inductance \( M \) of the square loop - long conductor pair changes with time \( t \) according to which of the following graphs?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is C

Mutual inductance \( M \) is a measure of the ability of one current-carrying conductor to induce a current in another conductor.
For a square loop moving away from a long current-carrying conductor, the mutual inductance is given by:
\( M = \mu_0 N \frac{a^2}{2R} \) 
where \( a \) is the side length of the square loop, 
\( R \) is the distance between the conductor and the loop, and 
\( N \) is the number of turns. 

As the square loop moves away from the conductor, the distance \( R \) increases, resulting in a decrease in mutual inductance over time.