Two uniformly charged spherical conductors A and B of radii $5 m m$ and $10 m m$ are separated by a distance of $2 m$ . 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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$2 : 1$

$1 : 2$

$1 : 1$

$1 : 4$

answer is B.

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Detailed Solution

$V_{A} = V_{B}$
$\frac{{KQ}_{A}}{R_{A}} = \frac{{KQ}_{B}}{R_{B}}$
$\frac{Q_{A}}{Q_{B}} = \frac{R_{A}}{R_{B}} = \frac{1}{2}$
$E_{A} = \frac{{KQ}_{A}}{R_{A}^{2}};$ $E_{B} = \frac{{KQ}_{B}}{R_{B}^{2}}$

$\frac{E_{A}}{E_{B}} = \frac{Q_{A}}{Q_{B}} \times \frac{{R_{B}}^{2}}{R_{A}^{2}} = \frac{R_{B}}{R_{A}} = \frac{2}{1}$

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