Two spherical conductors A and B of radii R and 2R respectively, are separated by a large distance. If some charge is given to both the spheres and later they are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surfaces of spheres A and B is

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4 :1

2 :1

1: 4

1: 2

answer is D.

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Detailed Solution

When the spherical conductors are connected by a conducting wire, charge is redistributed and the spheres attain a common potential V.

$∴ I n t e n s i t y E_{A} = \frac{1}{4 π ε_{0}} \frac{Q_{A}}{R_{A}^{2}} o r E_{A} = \frac{1 \times C_{A} V}{4 π ε_{0} R_{A}^{2}} = \frac{(4 π ε_{0} R_{A})}{4 π ε_{0} R_{A}^{2}} = \frac{V}{R_{A}}$

Similarly $E_{B} = \frac{V}{R_{B}}$

$∴ \frac{E_{A}}{E_{B}} = \frac{R_{B}}{R_{A}} = \frac{2 R}{R} = \frac{2}{1}$

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