If on the concentric hollow spheres of radii | vedclass

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Question

(d) ${q_1} + {q_2} = Q$ and $\frac{{{q_1}}}{{4\pi {r^2}}} = \frac{{{q_2}}}{{4\pi {R^2}}}$ (given)
${q_1} = \frac{{Q{r^2}}}{{{R^2} + {r^2}}}$ and ${q_

Vedclass · Accepted Answer

$\frac{{Q(R + r)}}{{4\pi {\varepsilon _0}({R^2} + {r^2})}}$

Vedclass · Answer

(d) ${q_1} + {q_2} = Q$ and $\frac{{{q_1}}}{{4\pi {r^2}}} = \frac{{{q_2}}}{{4\pi {R^2}}}$ (given)
${q_1} = \frac{{Q{r^2}}}{{{R^2} + {r^2}}}$ and ${q_2} = \frac{{Q{R^2}}}{{{R^2} + {r^2}}}$
Potential at common centre
$\frac{1}{{4\pi {\varepsilon _0}}}\left[ {\frac{{Q{r^2}}}{{({R^2} + {r^2})r}} + \frac{{Q{R^2}}}{{({R^2} + {r^2})R}}} \right] = \frac{{Q(R + r)}}{{4\pi {\varepsilon _0}({R^2} + {r^2})}}$

If on the concentric hollow spheres of radii $r$ and $R( > r)$ the charge $Q$ is distributed such that their surface densities are same then the potential at their common centre is

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