A small conducting sphere of radius is isolated in space and carries an excess charge of
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A small conducting sphere of radius R is isolated in space and carries an excess charge of +6q. Because the sphere is a conductor in electrostatic equilibrium, all excess charge resides on its surface and the electric field inside the metal is zero. A separate point charge of −q is fixed at a distance of 4R directly to the right of the sphere’s center along the horizontal axis.
Several points are identified along the same axis:
• Point K at the sphere’s center.
• Point L on the surface of the sphere at the rightmost edge.
• Point M located a distance 2R to the right of the sphere’s surface (i.e., 3R from the center).
Answer the following qualitatively.
(a) For each point (K, L, and M), state whether the magnitude of the electric field is zero, non-zero and finite, or undefined (infinite). Provide a brief justification in each case.
(b) Rank the magnitudes of the non-zero electric fields at points L and M from greatest to least, and justify your ordering using appropriate reasoning about distance and vector superposition.
(c) For points L and M, indicate the direction of the net electric field relative to the center of the sphere (toward the sphere’s center, away from it, or neither of these). Explain how the presence of both the sphere’s charge and the external point charge determines each direction.