NEET Physics Question - Electromagnetic Induction

A small square loop of wire of side l is placed inside a large square loop of wire of side L ( L > l ). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to :

l / L

l² / L

L/l

L²/l

Solution:

The mutual inductance M is found by calculating the magnetic flux through the small loop due to the current $I$ in the large loop. Using the formula for the magnetic field at the center of a square loop, $B \propto \frac{I}{L}$ .

Since the small loop is much smaller than the large one \( $L \gg l$ )\, the field is approximately uniform across its area \ $A = l^2$ . The flux $\Phi = B \cdot A$ is therefore proportional to \ $\frac{I}{L} \cdot l^2$ .

Because $M = \frac{\Phi}{I}$ , the mutual inductance scales as:

M \propto \frac{l^2}{L}

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Solution:

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