GATE PH 2025 Paper 1 — page 19

Questions 55–57 of 65. Imported answers require review unless explicitly marked reviewed.

Consider the integral

where

is a complex variable and

are positive real numbers. The integral is taken over a unit circle with center at the origin. Which of the following option(s) is/are correct?

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

when

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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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A point charge

is placed at the origin, inside a linear dielectric medium of infinite extent, having relative permittivity

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

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

The magnitude of the polarization varies as

The magnitude of the screened charge due to the dielectric medium is less than the magnitude of the point charge

for

The magnitude of the screened charge due to the dielectric medium is more than the magnitude of the point charge

for

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2025 · Paper 1