Question

A long straight wire carries a current of $50A$. An electron moving at ${10}^{7}m/s$ is $5cm$ away from the wire. The force acting on electron if its velocity is directed towards the wire will be :

• A. $1.6\times {10}^{-6}N$
• B. $3.2\times {10}^{-16}N$
• C. $4.8\times {10}^{-16}N$
• D. $1.8\times {10}^{-16}N$

Answer 1

Answer: (B)

$3.2\times {10}^{-16}N$

Given: Current in wire= 50A

Speed of electron=${10}^{7}m{s}^{-1}$

Solution: Let us assume the current is directed in +y direction.

As we know, magnetic field due to straight wire is given by,

$B=\frac{{\mu }_{0}i}{2\pi r}$

$=\frac{4\pi \times {10}^{-7}\times 50}{2\pi \times 0.05}$

$=0.0002T$

According to question, v and B are perpendicular to each other.

$F=qvb$

Substituting the values we get,

$=1.6\times {10}^{-19}\times {10}^7\times 0.0002$

$=3.2\times {10}^{-16}N$

Hence, the correct option is (B).