Question

Two conducting spheres each of radius R carry charge q. They are placed at a distance r from each other, where r > > 2R. The neutral point lies at a distance r/2 from either sphere. If the electric field at the neutral point due to either sphere be E, then the total electric potential at that point will be

Moderate

Solution

$E = \frac{1}{4 {πε}_{0}} \times \frac{q}{(r / 2)^{2}}$
and $V = \frac{1}{4 {πε}_{0}} \times \frac{q}{(r / 2)}$
$∴ r = \frac{V}{E} or V = rE$

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