Physics · Potential difference, equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field

A diverging electron beam enters a region of varying potentials. Intersection of

A diverging electron beam enters a region of varying potentials. Intersection of equispaced equipotential plane surfaces with the plane of the paper are shown, with their potentials mentioned in the figure. If before entering this region, \( x \) and \( y \) components of the velocity of electrons \( \operatorname{are} 3 \sqrt{\frac{2 e v}{m}} \) and \( \sqrt{\frac{e v}{m}}, \) respectively, where \( m \) is the mass of an electron and \( e \) is the electronic charge, then : This question has multiple correct options

  • A. the electron beam is converged
  • B. the electron beam is diverged
  • C. the electric field is uniform and is directed towards negative x-axis
  • D. the electric field is uniform and is directed towards positive x-axis

Step-by-step solution

The electric field is uniform and directed perpendicular to equipotential surfaces. The given initial velocities show the beam is moving primarily in the x-direction. If the electric field is directed towards negative x-axis, the force on electrons is towards positive x, accelerating them. This increases the x-component of velocity, reducing the divergence angle and causing the beam to converge. Thus, option A is correct.
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