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A coil of single turn is wound on a sphere of radius $R = 1 m$ and mass $m = 2 k g$ . The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is $I = 4 A$ . Find the magnitude of uniform magnetic induction $B$ if the sphere is in equilibrium as shown in figure. $[g = 10 m / s^{2}]$

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$(\frac{2}{π}) T$

$(\frac{4}{π}) T$

$(\frac{3}{π}) T$

$(\frac{5}{π}) T$

answer is D.

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Detailed Solution

$τ_{p} = 0 τ_{m g \sin θ} + τ_{B} = 0 \Rightarrow B = \frac{(m g)}{π / R} = \frac{2 \times 10}{(π) (4) \times 1} B = (\frac{5}{π}) T$

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