Question

II. When a charged particle enters in a transverse magnetic field then:

• A. ed particle remains constant.
• B. constant.

Answer 1

Answer: (A)

The kinetic energy of the charged particle remains constant, but its momentum changes.

Answer 2

When a charged particle enters a transverse magnetic field, the magnetic force acting on it is given by: $\vec{F} = q(\vec{v} \times \vec{B})$

1. Work done by magnetic force: The magnetic force $\vec{F}$ is always perpendicular to the velocity $\vec{v}$ of the particle. Therefore, the work done by the magnetic force is zero ($W = \vec{F} \cdot \vec{dr} = 0$, since $\vec{F} \perp \vec{dr}$).

2. Kinetic Energy: According to the work-energy theorem, the change in kinetic energy is equal to the net work done on the particle. Since the magnetic force does no work, and assuming no other forces are acting, the kinetic energy ($KE = \frac{1}{2}mv^2$) of the charged particle remains constant. This implies that the magnitude of the velocity ($v$) of the particle remains constant.

3. Momentum: Momentum is a vector quantity, $\vec{p} = m\vec{v}$. While the magnitude of the velocity ($v$) remains constant, the magnetic force continuously changes the direction of the velocity vector. Since the direction of $\vec{v}$ changes, the momentum vector $\vec{p}$ also changes.

Therefore, when a charged particle enters a transverse magnetic field, its kinetic energy remains constant, but its momentum changes.

Explanation of the solution: The magnetic force on a charged particle is always perpendicular to its velocity, so it does no work. Consequently, the kinetic energy (and thus the speed) of the particle remains constant. However, since the force continuously changes the direction of the particle's velocity, its momentum (a vector quantity) changes.