For the situation shown in the figure below, mark out the correct… - Vidyadip

MCQ

For the situation shown in the figure below, mark out the correct statement

A
Potential of the conductor is $\frac{{ - q}}{{4\pi {\varepsilon _0}\left( {d + R} \right)}}$
B
Potential of the conductor is $\frac{q}{{4\pi {\varepsilon _0}d}}$
C
Potential of the conductor can’t be determined as nature of distribution of induced charges is not known
✓
Potential at point $B$ due to induced charges is $\frac{{ - qR}}{{4\pi {\varepsilon _0}\left( {d + R} \right)d}}$

✓

Answer

Correct option: D.

Potential at point $B$ due to induced charges is $\frac{{ - qR}}{{4\pi {\varepsilon _0}\left( {d + R} \right)d}}$

d
Potential at surface $=$ Potential at centre

$\mathrm{V}_{\mathrm{+q}}+\mathrm{V}_{\mathrm{ind}}=\mathrm{V}_{\mathrm{c}}$

$\mathrm{V}_{\mathrm{ind}}=\frac{\mathrm{Kq}}{(\mathrm{R}+\mathrm{d})}-\frac{\mathrm{Kq}}{\mathrm{d}}=\frac{-\mathrm{qR}}{4 \pi \varepsilon_{0}(\mathrm{d}+\mathrm{R}) \mathrm{d}}$

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