(D) Let the charge on the sphere be $Q$. The potential at the surface of the sphere is $V_{surface} = \frac{kQ}{r}$. The potential at a distance $3r$

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(D) Let the charge on the sphere be $Q$. The potential at the surface of the sphere is $V_{surface} = \frac{kQ}{r}$. The potential at a distance $3r$ from the center is $V_{3r} = \frac{kQ}{3r}$. The potential difference $V$ is given by: $V = V_{surface} - V_{3r} = \frac{kQ}{r} - \frac{kQ}{3r} = \frac{2kQ}{3r}$. From this,we find $kQ = \frac{3Vr}{2}$. The electric intensity $E$ at a distance $3r$ from the center is given by: $E = \frac{kQ}{(3r)^2} = \frac{kQ}{9r^2}$. Substituting the value of $kQ$: $E = \frac{1}{9r^2} \cdot \frac{3Vr}{2} = \frac{3V}{18r} = \frac{V}{6r}$.

Class 12 Physics Electric Potential and Capacitance Mix Examples - Electric Potential and Capacitance

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$A$ hollow metal sphere has a radius $r$. The potential difference between a point on its surface and a point at a distance $3r$ from its center is $V$. The electric intensity at the distance $3r$ from the center of the sphere will be

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A
$\frac{V}{3r}$
B
$3Vr$
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$\frac{V}{r}$
D
$\frac{V}{6r}$

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Mix Examples - Electric Potential and Capacitance

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$A$ hollow metal sphere has a radius $r$. The potential difference between a point on its surface and a point at a distance $3r$ from its center is $V$. The electric intensity at the distance $3r$ from the center of the sphere will be

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