Question

Two thin long parallel wires separated by a distance 'b' are carrying a current i A each. The magnitude of the force per unit length exerted by one wire on the other is?

• A. $\frac{{\mu }_o{i}^2}{b^2}$
• B. $\frac{{\mu }_o{i}^2}{2\pi b}$
• C. $\frac{{\mu }_{o}i}{2\pi b}$
• D. $\frac{{\mu }_{o}i}{2\pi b^2}$

Answer 1

Answer: (B)

$\frac{{\mu }_o{i}^2}{2\pi b}$

Given, distance between two parallel wires$=b$ and current flowing in both the wire$=i$

Now we know force of attraction between two parallel current carrying conductors is given by

$F=\frac{\mu 2I_1{I}_{2}l}{4\pi b}$---------(A)

Here$I_1=I_2$ as per question,

Thus equation A reduces to

$\frac{F}{l}=\frac{{\mu }_0{i}^2}{2\pi b}$