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Q.

Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B will be :

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a

1 : 4

b

2 : 1

c

1 : 2

d

1 : 1

answer is B.

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Detailed Solution

$\begin{array}{l} V_{A} = V_{B} \\ \frac{{KQ}_{A}}{R_{A}} = \frac{{KQ}_{B}}{R_{B}} \\ \frac{Q_{A}}{Q_{B}} = \frac{R_{A}}{R_{B}} = \frac{1}{2} \\ E_{A} = \frac{{KQ}_{A}}{R_{A}^{2}}; E_{B} = \frac{{KQ}_{B}}{R_{B}^{2}} \\ \frac{E_{A}}{E_{B}} = \frac{Q_{A}}{Q_{B}} \times \frac{{R_{B}}^{2}}{R_{A}^{2}} = \frac{R_{B}}{R_{A}} = \frac{2}{1} \end{array}$

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Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B will be :