Question

When a charged particle enters a magnetic field in a direction perpendicular to the field, which one of the following does not change?

• A. Kinetic energy
• B. Velocity
• C. Force
• D. Momentum

Answer 1

The correct option is A

Kinetic energy

Magnetic Force:

1. A magnetic force is generated by a charged particle when it encounters a magnetic field.
2. A charged particle in a magnetic field travels a curved route because the magnetic force is perpendicular to the travel direction.
3. The formula for calculating magnetic force is as follows: $\overrightarrow{\mathrm{F}}=\mathrm{q}(\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}})$.
4. The force's magnitude would be given as $\mathrm{F}=\mathrm{qvBsin}\left(\mathrm{\theta }\right)$.
5. Since the charged particle is traveling in a perpendicular direction to the field, the amount of the force changes.
   $$\begin{gathered} \mathrm{F}=\mathrm{qvBsin}\left({90}^0\right) \\ =\mathrm{qvB} \end{gathered}$$
6. As the direction of the force is perpendicular to the direction of the particle's velocity or displacement, the work done on the particle by the magnetic field is zero, and the Work-Energy theorem states that the change in kinetic energy is also zero, we can conclude that the particle's kinetic energy remains constant.
7. Thus, kinetic energy does not change.

The explanation for the correct option:

1. The velocity changes when it enters as it enters the magnetic field from the above equation.
2. So therefore even the momentum which is the product of mass and velocity will change.
3. The change in the force is given in the above question.

Therefore, option A is the correct choice.