GATE PH 2024 Paper 1 — page 16

Questions 46–48 of 65. Imported answers require review unless explicitly marked reviewed.

Two point charges of charge

each are placed a distance

apart. A grounded solid conducting sphere of radius

is placed midway between them. Assume

. Which of the following statement is/are true?

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

, the net force acting on the charges is directed towards each other

The potential at the surface of the sphere is zero

Total induced charge on the sphere is

The potential at the center of the sphere is non-zero

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A particle of mass

is moving in the potential

Figures P, Q, R and S show different combinations of the values of

and

and

with

are the eigen-energies of the

-th level for the potentials shown in figures P, Q, R and S, respectively. Which of the statement is/are true?

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

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The non-relativistic Hamiltonian for a single electron atom is

where

is the Coulomb potential and

is the mass of the electron. Considering the spin-orbit interaction term

added to

, which of the following statement is/are true?

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

commutes with

and

For a given value of principal quantum number

and orbital angular momentum quantum number

, there are

degenerate eigenstates of

and

have a set of simultaneous eigenstates

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2024 · Paper 1