Q. Cathode rays of velocity $10^{6}\ ms^{- 1}$ describe an approximate circular path of radius 1 m in an electric field of $500\ V\ cm^{- 1}$. If the velocity of cathode rays is doubled, the value of electric field needed so that the rays describe the same circular path is
A) $1000\ V\ cm^{- 1}$
B) $1500\ V\ cm^{- 1}$
C) $2000\ V\ cm^{- 1}$
D) $500\ V\ cm^{- 1}$
Explanation
(c) $eV = mv^{2}/r;$ so $V \propto v^{2};$
$\therefore\ \ V_{2} = V_{1}\left( \frac{v_{2}}{v_{1}} \right)^{2} = 500\left( \frac{2v}{v} \right)^{2} = 2000V\ cm^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.