When an electron is passing through magnetic field, then :

Question

Accepted Answer

When an electron is passing through a magnetic field, its velocity and energy remain constant. This is because a magnetic field exerts a force on a charged particle like an electron only when it is moving perpendicular to the field. This force is known as the Lorentz force, and it acts perpendicular to both the velocity of the electron and the magnetic field. As a result, the force does not do any work on the electron.

1. **Explanation for Option 4 (Correct Answer):**  
   The work done by a force is calculated as the dot product of the force and the displacement in the direction of the force. Since the magnetic force is always perpendicular to the velocity of the electron, the displacement in the direction of the force is zero. Therefore, the work done by the magnetic force is zero, meaning there is no change in the kinetic energy of the electron. Consequently, both the velocity (in terms of magnitude) and energy of the electron remain constant as it moves through the magnetic field.

2. **Explanation for why Option 1 is incorrect:**  
   Option 1 suggests that the velocity of the electron is increased. However, since the magnetic force does not do work on the electron, it cannot change the magnitude of the electron's velocity. The velocity vector may change direction due to the perpendicular force, but its magnitude remains constant.

3. **Explanation for why Option 2 is incorrect:**  
   Option 2 suggests that the energy of the electron is increased. The energy of the electron, specifically its kinetic energy, remains constant because the magnetic force does no work on the electron. Since there is no work done, there is no change in energy.

4. **Explanation for why Option 3 is incorrect:**  
   Option 3 suggests that both velocity and energy are increased. As explained above, the magnetic force does not change the magnitude of the velocity or the energy of the electron. The force only changes the direction of the velocity, not its magnitude, and does not affect the energy.

In conclusion, the correct answer is Option 4 because the magnetic field does not do work on the electron, leaving both its velocity and energy unchanged.