A metallic solid sphere of radius R is given the charge Q. Which of the followingstatement is true then(a) Electric field at points 0< r < R is zero(b) Charge Q is on the outer surface of the sphere(c) Electric field at r>R is given by Q/4πε0r2(d) Electric field is perpendicular to the surface of the sphere
Question
A metallic solid sphere of radius R is given the charge Q. Which of the followingstatement is true then(a) Electric field at points 0< r < R is zero(b) Charge Q is on the outer surface of the sphere(c) Electric field at r>R is given by Q/4πε0r2(d) Electric field is perpendicular to the surface of the sphere
Solution
(a) True. Inside a uniformly charged metallic sphere, the electric field is zero. This is because the charges distribute themselves on the surface of the sphere and there is no net charge inside the sphere.
(b) True. In a metallic sphere, the charges reside on the surface of the sphere. This is due to the fact that the charges repel each other and try to get as far away from each other as possible, which is on the surface of the sphere.
(c) True. Outside the sphere, it behaves as if all the charge is concentrated at the center of the sphere. So, the electric field at a distance r from the center of the sphere is given by Coulomb's law, E = Q/4πε0r^2.
(d) True. The electric field is always perpendicular to the surface of the conductor. This is because the electric field inside a conductor is zero, and the field lines must be perpendicular to the surface at the boundary between the conductor and the outside.
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