# A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

Question:

A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R(R>r)$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

1. $\frac{1}{4 \pi \varepsilon_{0}} \frac{(R+r)}{2\left(R^{2}+r^{2}\right)} Q$

2. $\frac{1}{4 \pi \varepsilon_{0}} \frac{(2 R+r)}{\left(R^{2}+r^{2}\right)} Q$

3. $\frac{1}{4 \pi \varepsilon_{0}} \frac{(R+2 r) Q}{2\left(R^{2}+r^{2}\right)}$

4. $\frac{1}{4 \pi \varepsilon_{0}} \frac{(R+r)}{\left(R^{2}+r^{2}\right)} Q$

Correct Option: 4

Solution:

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