A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0≤r<∞, where r is the distance from the centre of the shell?
(A)(see graph)✓ Correct
(B)(see graph)
(C)(see graph)
(D)(see graph)
Answer: (A)
Solution
By Gauss's law a uniformly charged spherical shell encloses no charge for points inside it, so the field is exactly zero throughout r<R. At the surface the full charge is enclosed and the field jumps to 4πε0R2Q, and for r>R the shell behaves like a point charge at the centre, the field falling as 4πε0r2Q. The graph that stays at zero up to r=R, rises abruptly there, and then decays as 1/r2 is the one that matches.
JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option