The below are the diagrams showing the entry of an electron (e-) in a magnetic field (B). The diagram which shows the minimum force on the electron is

# The below are the diagrams showing the entry of an electron $\left({e}^{-}\right)$ in a magnetic field $\left(B\right)$. The diagram which shows the minimum force on the electron is

1. A

2. B

3. C

4. D
None of the above

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### Solution:

The diagram which shows the minimum force on the electron is option 3.
When a particle carrying charge $q$ is moving with a velocity $v$ in a magnetic field $B$, a force is exerted on it. This force can be calculated by using the equation $F=q\left(v×B\right)$. Since it is a cross product, $F=\mathit{qvBsin\theta }$, where $\theta$ is the angle between $v$ and $B$. Therefore, the force is minimum when $\theta =0$ and maximum when $\theta =9{0}^{o}$. The condition for minimum force is when the particle moves in the direction of the field and that for maximum force is when the particle moves in the direction perpendicular to the field. Since the figure in option 3 clearly shows the particle moving in the direction of the field, the force on the particle there is minimum.

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