Question

An electron is projected into a magnetic field of $B=5\times {10}^{-3}T$ and rotates in a circle of radius of $R=3mm$ . Find the work done by the force due to the magnetic field.

• A. $0mJ$
• B. $15mJ$
• C. $14mJ$
• D. $20mJ$

Answer 1

The correct option is A

$0mJ$

Step 1. Given data:

Magnetic field, $B=5\times {10}^{-3}T$,

The radius of the circular path on which electron rotates, $R=3mm$$=3\times {10}^{-3}m$ ,

Charge on the electron which introduce force, $q=1.6\times {10}^{-19}C$,

Work done by the force on the magnetic field, $W=?$,

Step 2. Calculating work done:

$W=F.dS$ [$F$ is force, $dS$ is displacement]

Magnetic force is perpendicular to the displacement. The electron is moving in a circular path.

Displacement, $dS=0$. As the displacement of the circular path is zero.

$\therefore W=0$

Therefore, the work done by the force due to the magnetic field is $\mathbf{0}\mathbf{}\mathit{m}\mathit{J}$.

Hence, the correct option is $\left(A\right)$.