GATE PH 2025 PH Q56: Electromagnetic Theory

A neutral conducting sphere of radius

is placed in a uniform electric field of magnitude

, that points along the

axis. The electrostatic potential at any point

outside the sphere is given by

, where

is the constant potential of the sphere. Which of the following option(s) is/are correct?

Your answerSelect all correct options. You can choose more than one.

The induced surface charge density on the sphere is proportional to

The electric field at any point is curl free for

The electric field at any point is divergence free for

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