Question

Two long thin parallel conductor 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 conductor is undeflected. lf $c$ is the velocity of light. then :

• A. $v=\frac{\lambda c^2}{i}$
• B. $v=\frac{i}{\lambda }$
• C. $c=\frac{i}{\lambda }$
• D. the electron may be at any distance from the conductor

Answer 1

Answer: (A), (D)

The correct options are
A the electron may be at any distance from the conductor
D $v=\frac{\lambda c^2}{i}$

Magnetic field due to long straight conductor at a distance $r$ is given by $B=\frac{{\mu }_{o}i}{2r}$
Magnitude of magnetic force acting on the electron $F_m=evB=\frac{{\mu }_{o}iev}{2r}$
Electric field due a straight charge carrying conductor $E=\frac{\lambda }{2\pi {ϵ}_{o}r}$
Electrostatic force acting on the electron $F_e=eE=\frac{e\lambda }{2\pi {ϵ}_{o}r}$
Since, electron do not get deflected. So, both the forces cancel out each other.
$\therefore$ $\frac{{\mu }_{o}iev}{2r}$ $=\frac{e\lambda }{2\pi {ϵ}_{o}r}$
Or $v=\frac{\lambda }{i{ϵ}_o{\mu }_o}$
Using $c^2=\frac{1}{{\mu }_o{ϵ}_o}$
$⟹v=\frac{\lambda c^2}{i}$
Since, the above relation is independent on the distance of electron i.e. $r$, so the electron can be at any distance from the conductor.