An electron enters in a magnetic field along perpendicular direction, then which of the following quantities related to electron will remain constant?

Question

Accepted Answer

When an electron enters a magnetic field perpendicularly, it experiences a force due to the magnetic field, which is perpendicular to both the velocity of the electron and the magnetic field itself. This force is known as the Lorentz force and is given by the equation $ F = q(v \times B) $, where $ q $ is the charge of the electron, $ v $ is its velocity, and $ B $ is the magnetic field.

1. **Explanation for Option 2 (Kinetic energy):**
   - The kinetic energy of the electron remains constant because the magnetic force does no work on the electron. The work done by a force is given by 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 is zero, and the kinetic energy, which depends on the speed of the electron, remains unchanged.

2. **Explanation for why other options are incorrect:**

- **Option 1 (Momentum):**
     - Momentum is a vector quantity given by the product of mass and velocity ($ p = mv $). While the speed of the electron remains constant, its direction changes continuously due to the perpendicular magnetic force. This change in direction means that the momentum vector changes, even though its magnitude (related to speed) remains constant.

- **Option 3 (Velocity):**
     - Velocity is also a vector quantity, and while the magnitude of the velocity (speed) remains constant, the direction of the velocity changes continuously as the electron moves in a circular path due to the magnetic force. Therefore, the velocity is not constant.

- **Option 4 (Acceleration):**
     - Acceleration is the rate of change of velocity. Since the direction of the velocity is changing continuously, the electron is undergoing centripetal acceleration. This acceleration is directed towards the center of the circular path and is not constant in direction, although its magnitude remains constant. Therefore, acceleration is not constant in terms of its vector nature.

In conclusion, the kinetic energy of the electron remains constant because the magnetic force does not do any work on the electron, ensuring that its speed, and thus its kinetic energy, remains unchanged.