A rod is moving with velocity 9 m/s perpendicular to external magnetic field of 1T and there is a conducting sphere having charge 30 C and radius R. If electric field inside rod is same as electric field on the surface of sphere and radius $R = x \times 10^{5}$ m then find x.
(Round off to nearest integer)

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Detailed Solution

Induced field in rod, E = vB
electric field on surface of sphere $= \frac{K Q}{R^{2}}$

$\frac{K Q}{R^{2}} = v B \Rightarrow R^{2} = \frac{k Q}{v B} = \frac{9 \times 10^{9} \times 30}{9 \times 1}$

$R = \sqrt{3} \times 10^{5} = 1.73 \times 10^{5}$

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