Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field and the electric potential V(r) with the distance r from the centre, is best represented by which graph?

Engineering

Physics

Electric Potential Energy and Electric Potential

Electric Field and Charged Particle in Electric Field

Question

Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $| \vec{E} (r) |$ and the electric potential V(r) with the distance r from the centre, is best represented by which graph?

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For a uniformly charged spherical shell of radius R:

Inside (r < R): Electric field is zero, $E = 0$ . Potential is constant and equal to its value at the surface, $V = \frac{1}{4 π ε_{0}} \frac{Q}{R}$ .

Outside (r > R): Field and potential are as if all charge Q is at the center. $E \propto \frac{1}{r^{2}}$ and $V \propto \frac{1}{r}$ .

At r = R, E is discontinuous (jumps from 0 to $\frac{1}{4 π ε_{0}} \frac{Q}{R^{2}}$ ), while V is continuous.

Final Answer: The second graph (top right) correctly shows E=0 inside and 1/r² outside, with V constant inside and 1/r outside.