Question

Two long, thin, parallel conductors are kept very close to each other, without touching. One carries a current i, and the other has charge $\lambda$ per unit length. An electron moving parallel to the conductors is un-deflected. Let C = velocity of light. Then,

• A. $v=\frac{\lambda c^2}{i}$
• B. $v=\frac{i}{\lambda }$
• C. $c=\frac{i}{\lambda }$
• D. $v-i\lambda$

Answer 1

The correct option is A $v=\frac{\lambda c^2}{i}$

At P, electric field
$=E=\frac{\lambda }{2\pi {\epsilon }_{0}x}$ to the right, and magnetic field =$B=\frac{{\mu }_{0}i}{2\pi x}$
(into the paper)$C=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
For no deflection E=vB, or $v=\frac{E}{B}$
or $v=\frac{\lambda }{2\pi {\epsilon }_{0}x}\times \frac{2\pi x}{{\mu }_{0}i}=\frac{\lambda }{i}\frac{1}{{\epsilon }_0{\mu }_0}=\frac{\lambda C^2}{i}$