Question

A charge $Q$ is moving $\overrightarrow{dl}$ distance in the magnetic field $\overrightarrow{B}$. Find the value of work done by $\overrightarrow{B}$

• A. Infinite
• B. $1$
• C. $-1$
• D. zero

Answer 1

The correct option is D

zero

Step 1: Given data

Charge $=Q$

Distance $=\overrightarrow{dl}$

Magnetic field $=\overrightarrow{B}$

$F=$ Force

$S=$Displacement

Step 2: To find the value of work done by $\overrightarrow{B}$

Since force on a point charge by the magnetic field $\overrightarrow{B}$ is always perpendicular to $\overrightarrow{V}$,

$\overrightarrow{F}=q\overrightarrow{V}\times \overrightarrow{B}$

As the displacement of the point, the charge is in the direction of the velocity of the charge, thus, the magnetic force acting on the charge is perpendicular to the direction of the displacement.

Thus, the work done is

$$\begin{gathered} W=F.S \\ W=F.S\cos \theta \\ W=F.S\cos {90}^{°} \\ W=F.S\times 0 \\ W=0 \end{gathered}$$ $\left[\because \theta =90°\right]$

Therefore, the work done is $\mathbf{0}$.

Hence, the correct answer is option (D).