Physics - Electrostatics Question with Solution | TestHub
A solid conducting sphere of radius R has a spherical cavity of radius 'a' (a < R) at its center. A point charge +q is placed at the center of the cavity. The conductor is initially uncharged. Match the following quantities with their correct values. (Take )
List - I | List - II |
|---|---|
(P) Charge induced on the inner surface of the cavity | (1) |
(Q) Charge induced on the outer surface of the conducting sphere | (2) |
(R) Magnitude of electric field at a distance a/2 from the center (inside cavity) | (3) |
(S) Electric potential at a distance R/2 from the center (inside conductor) | (4) |
Options:
Answer:
Solution:
For a conductor in electrostatic equilibrium, the electric field inside the conductor is zero, and the potential is constant throughout its volume.
P: By Gauss's Law, for a Gaussian surface within the conducting material (between 'a' and R), the electric field is zero. Thus, the net charge enclosed must be zero. If a point charge +q is at the center, the inner surface of the cavity must have an induced charge of -q. So (P)-(2).
Q: The conductor is initially uncharged. Since -q is induced on the inner surface, to maintain a net charge of zero on the conductor, a charge of +q must be induced on the outer surface. So (Q)-(1).
R: For a point inside the cavity (), only the point charge +q contributes to the electric field. At , . So (R)-(3).
S: For a point inside the conducting material (), the electric potential is constant and equal to the potential on the outer surface of the sphere. The potential on the outer surface is due to the net charge +q on the sphere (considering the internal charge +q and the induced charges -q and +q). Thus, . So (S)-(4).
