Mutual Induction: Practice Problem & Solution
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 :
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Mutual Induction. Understanding the underlying formula is key to arriving at the correct answer below:
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 \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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