Answer

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**Hint**The direction of the force of the magnetic field acting on a moving charge is given by the Right hand rule. Work is said to be done if a force is applied on a body through a distance which in the direction of the force

In this solution we will be using the following formula;

$\Rightarrow \vec F = q\vec v \times \vec B$ where $F$ is the magnetic force, $q$ is the charge of the particle, $\vec v$ is the velocity of the particle and $\vec B$ is the magnetic field in the region. The $ \times $ symbol in this case signifies a cross product. $W = \vec F \cdot \vec r$ where $W$ is the work done by the force $F$, and $r$ is the distance moved by the body while the force is being applied.

**Complete step by step answer**

When a body is in a magnetic field, the force exerted by the magnetic field is determined by

$F = q\vec v \times \vec B$ where $q$ is the charge of the particle, $\vec v$ is the velocity of the particle and $\vec B$ is the magnetic field in the region. The $ \times $ symbol in this case signifies cross product

This can be written in magnitude only form as

$\Rightarrow F = qvB\sin \theta $ where $\theta $ is the angle between the velocity $v$ and the field $B$. However since cross product is involved, the direction of the force $F$ is always perpendicular to both the field and the velocity, as given by the Right hand rule. Since $v$ and $r$ are always in the same direction, then $F$ is perpendicular to $r$.

Now work is only done when the distance moved by the object is, or has a component, parallel to the force.

Hence, since they are perpendicular (no component parallel) the work done is Zero.

**Hence, the correct option is C.**

**Note**

Alternatively, in mathematical terms, since work is given as

$\Rightarrow W = \vec F \cdot \vec r$ and $r = vt$

Hence, by replacement

$\Rightarrow W = \vec F \cdot \vec vt$. Work can be written as

$\Rightarrow W = Fvt\cos \theta $ where $\theta $ is the angle between $v$ and $F$.

Since they are perpendicular, then $\theta = 90^\circ $

Hence.

$\Rightarrow W = Fvt\cos 90 = 0$

$\therefore W = 0$.

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