List of top Physics Questions on Electric Charge asked in GATE PH

Two point charges of charge \( +q \) each are placed a distance \( 2d \) apart. A grounded solid conducting sphere of radius \( a \) is placed midway between them. Assume \( a^2 \ll d^2 \). Which of the following statements is/are true?

A particle of mass \( m \) in an infinite potential well of width \( a \) is subjected to a perturbation \( V' = \frac{h^2}{40ma^2} \) as shown in the figure, where \( h \) is Planck's constant.

The first-order energy shift of the fourth energy eigenstate due to this perturbation is \( \frac{h^2}{Nma^2} \). The value of \( N \) is ____ (in integer).

An electron in the Coulomb field of a proton is in the following state of coherent superposition of orthonormal states \( \psi_{n i m} \):\[ \psi = \frac{1}{3} \psi_{100} + \frac{1}{\sqrt{3}} \psi_{210} + \frac{\sqrt{5}}{3} \psi_{320} \]Let \( E_1, E_2, \) and \( E_3 \) represent the first three energy levels of the system. A sequence of measurements is done on the same system at different times. Energy is measured first at time \( t_1 \) and the outcome is \( E_2 \). Then total angular momentum is measured at time \( t_2 > t_1 \), and finally, energy is measured again at \( t_3 > t_2 \). The probability of finding the system in a state with energy \( E_2 \) after the final measurement is \( \frac{P}{9} \). The value of \( P \) is ______ (in integer).

The curves \( P \) and \( Q \) schematically show the variation of X-ray intensity with wavelength at two different accelerating voltages for a given target material. In the figure, \( \lambda_1 = 0.25 \) Å, \( \lambda_2 = 0.5 \) Å, \( \lambda_3 = 1.0 \) Å, and \( \lambda_4 = 2.25 \) Å. Take Planck's constant as \( 6.6 \times 10^{-34} \) Js, the speed of light as \( 3 \times 10^8 \) m/s, and the elementary charge as \( 1.6 \times 10^{-19} \) C.

Which of the following statement is/are true?