Electromagnetic Induction and Alternating Current 3 Question 6
####7. 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
(1998, 2M)
(a) $l / L$
(b) $l^{2} / L$
(c) $L / l$
(d) $L^{2} / l$
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Answer:
Correct Answer: 7. (b)
Solution:
- Magnetic field produced by a current $i$ in a large square loop at its centre,
$$ B \propto \frac{i}{L} \quad \text { say } \quad B=K \frac{i}{L} $$
$\therefore$ Magnetic flux linked with smaller loop,
$$ \begin{aligned} & \varphi=B \cdot S \\ & \varphi=K \frac{i}{L}\left(l^{2}\right) \end{aligned} $$
Therefore, the mutual inductance
$$ M=\frac{\varphi}{i}=K \frac{l^{2}}{L} \quad \text { or } \quad M \propto \frac{l^{2}}{L} $$
NOTE Dimensions of self inductance (L) or mutual inductance $(M)$ are [Mutual inductance] $=$ [ Self inductance]
$$ \left.=\left[\mu_{0}\right] \text { [length }\right] $$
Similarly, dimensions of capacitance are
[capacitance $]=\left[\varepsilon_{0}\right]$ [length $]$
From this point of view, options (b) and (d) may be correct.
