An infinitely long straight conductor carries a current of 5A as shown. An electron is moving with a speed of $10^5 m/s$ parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

(1) $4\times 10^{-20}N$
(2) $8\pi \times 10^{-20}N$
(3) $4\pi \times 10^{-20}N$
(4) $8\times 10^{-20}N$

Solution

Magnetic field due to wire $B=\frac {\mu_0}{4\pi}\frac {2I}{r}$

Force on electron $=evB=ev\frac {\mu_0}{4\pi}\frac {2I}{r}=10^{-7}\times 1.6\times 10^{-19}\times 10^5 \times 2\times \frac {5}{0.2}=8\times 10^{-20}N$

Answer: Option (4)