Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is :

1 : 4

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4 : 1

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1 : 2

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2 : 1

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Solution

The correct option is D 2 : 1
Electric field at the surface of sphere of radius R is $E = k Q / R^{2}$
When two spherical conductors are connected by wire, the charge will flow from higher potential to lower potential till they will get same potential i.e equilibrium.
Thus,
$V_{A} = V_{B}$ or
$k Q_{A} / R_{A} = k Q_{B} / R_{B}$
Thus, $\frac{E_{A}}{E_{B}} = \frac{R_{B}}{R_{A}} = \frac{2}{1}$
so, option D

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