Magnetic force on a moving charge

When a charged particle moves in a magnetic field, the magnetic force is $\vec{F} = q\,\vec{v} \times \vec{B}.$

Since the particle moves perpendicular to the magnetic field, the angle between $\vec{v}$ and $\vec{B}$ is $90^\circ$, so the magnitude of force is $F = qvB.$

Direction of magnetic force

The magnetic force is always perpendicular to the velocity $\vec{v}$.

Therefore, it can change only the direction of motion, not the speed.

Effect on kinetic energy

Kinetic energy is $K = \frac{1}{2}mv^2.$

Since the speed $v$ remains constant, the kinetic energy remains constant.

Effect on momentum

Momentum is $\vec{p} = m\vec{v}.$

Although the magnitude $p = mv$ remains constant, the direction of $\vec{p}$ changes continuously due to the magnetic force.

Hence, the momentum vector is not constant.

Option-wise conclusion

• A: Kinetic energy changes but momentum is constant → False
• B: Momentum changes but kinetic energy is constant → True
• C: Both momentum and kinetic energy are not constant → False
• D: Both momentum and kinetic energy are constant → False

Final answer

The correct option is: $\boxed{\text{B}}$