Question

A charged particle is projected in magnetic field $\overrightarrow{B}=10\hat{k}$ from origin in $x-y$ plane. The particle moves in a circle and just touches a line $y=5$ m at $x=5\sqrt{3}$ m. Then (mass of particle = $5 \times 10^{-5}$ kg, charge = $1\mu c$) -

• A. The particle is projected at an angle $60^\circ$ with $x$-axis
• B. The radius of circle is 10 m
• C. speed of particle is 2 m/s
• D. workdone by magnetic force on the particle is zero.

Answer 1

Answer: (D)

Workdone by magnetic force on the particle is zero.

Answer 2

The magnetic force $\vec{F} = q \, \vec{v} \times \vec{B}$ is always perpendicular to the velocity $\vec{v}$ of the particle. Since work done is given by:

$$W = \int \vec{F}\cdot d\vec{s},$$

and $\vec{F}$ is perpendicular to displacement $d\vec{s}$ (in the direction of $\vec{v}$), the dot product is zero.

Thus, the work done by the magnetic force is zero.