Question

A charged particle is projected in magnetic field $\overline{B}=10\hat{k}$ T from origin in X-Y plane. The particle moves in a circle and just touches a line y = 5m at $x=5\sqrt{3}m.$ Then (mass of particle $=5\times {10}^{-5}kg$ and 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 2m/s
  
• D. Work done by magnetic force on the particle is zero.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
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 2m/s

D

Work done by magnetic force on the particle is zero.

$R^2-(R-5{)}^2=(5\sqrt{3}{)}^2{R}^2-R^2(R-5{)}^2=(5\sqrt{3}{)}^2{R}^2-R^2-25+10R=75R=10msin\alpha =\frac{1}{2},\alpha ={30}^{\circ },\theta =90-\alpha ={60}^{\circ }\frac{mv}{qB}=R\Rightarrow v=\frac{RqB}{m}=\frac{10\times {10}^{-6}\times 10}{5\times {10}^{-5}}=2m/s$