Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of

Question

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the centre?

Accepted Answer

Given: A charged spherical conductor of radius $R$ . We need the graph of electric potential $V$ as a function of radial distance $r$ from the centre.

Find: Which option correctly represents the variation of $V$ with $r$ .

For a charged spherical conductor, the electric potential is constant inside the conductor and equal to the potential at the surface. For points outside the conductor, the potential behaves as

V = \frac{kQ}{r}

Therefore,

V = \frac{kQ}{R} \quad \text{for} \quad r \le R

and

V = \frac{kQ}{r} \quad \text{for} \quad r > R

So the graph must be a horizontal line from $r = 0$ to $r = R$ , and then it must decrease as $\frac{1}{r}$ for $r > R$ .

This matches option D in the solution's labeling, which corresponds to the 4th option in the given list.

Therefore, the correct option is D.

Given: The object is a spherical conductor, not an insulator.

Find: The shape of the $V$ versus $r$ graph.

Inside a conductor in electrostatic equilibrium, the electric field is zero. Since electric potential does not change where electric field is zero, the potential remains the same throughout the interior.

Hence, from the centre up to the surface at $r = R$ , the potential is constant. After the surface, the conductor behaves like a point charge for potential, so

V \propto \frac{1}{r}

for the outside region.

Thus the required graph is flat for $r \le R$ and then falls for $r > R$ . Therefore, the correct option is D.

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