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  4. Two conducting spheres each of radius R carry charge q. They are placed at a distance r from each other, where r > 2 R. 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:

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Q. Two conducting spheres each of radius $R$ carry charge $q$. They are placed at a distance r from each other, where $r \,>\, 2 R$. 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:

Electrostatic Potential and Capacitance

Solution:

$E = \frac{1}{4 \, \pi \, \varepsilon_0} \frac{q}{(r/2)^2} , V = 2 \left[ \frac{1}{4 \, \pi \, \varepsilon_0} \frac{q}{(r/2)} \right] $ Therefore $\frac{V}{E} = r$ . Hence $V = rE.$