Question

A charged particle of mass $2\text{kg}$ and charge $2\text{C}$ moves with a velocity $\overrightarrow{v}=8\hat{i}+6\hat{j}\text{m/s}$ in a magnetic field $\overrightarrow{B}=2\hat{k}\text{T}$. Then

• A. The path of particle may be $x^2+y^2=25$
• B. The path of particle may be $x^2+z^2=25$
• C. The time period of particle will be $3.14\text{s}$.
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A The path of particle may be $x^2+y^2=25$
C The time period of particle will be $3.14\text{s}$.

Since the magnetic field is in the z-direction, particle will execute circular motion is in x-y plane.

Radius of the particle's circular motion
$r=\frac{mv}{qB}=\frac{2kg\times 10m/s}{2C\times 2T}$
$=5m$
Hence (A) is correct.

Time period of particle's circular motion
$T=\frac{2\pi m}{Bq}=3.14\text{sec}$ (C)