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Offline Centres

A small square loop of wire of side ‘l’ is placed inside a Large square Loop of wire L(L>>l). Both Loops are coplanar and their centres coincide at point ‘O’ as shown in the figure. The mutual inductance of the system is

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$\frac{2 \sqrt{2} μ_{0} L^{2}}{π l}$

$\frac{2 \sqrt{2} μ_{0} l^{2}}{π L}$

$\frac{μ_{0} L^{2}}{2 \sqrt{2} π l}$

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Detailed Solution

$B^{1} = 4 B = 4 \frac{μ_{0} i}{4 π (\frac{L}{2})} (2 \sin 45^{0})$

$B^{1} = \frac{2 \sqrt{2} μ_{0} i}{π L}$

$M = \frac{F l u x i n n e r l o o p}{i} = \frac{2 \sqrt{2} μ_{0} i l^{2}}{i π^{2}}$

$= \frac{2 \sqrt{2} μ_{0} l^{2}}{π L}$

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