Question

A semi circular arc of radius r and a straight wire along the diameter, both are carrying same current i. Find out magnetic force per unit length on the small element P, which is at the centre of curvature?

• A. $\left(\frac{{\mu }_0{i}^2}{4r}\right)$
• B. $\left(\frac{{\mu }_0{i}^2}{2r}\right)$
• C. $\left(\frac{{\mu }_0{i}^2}{r}\right)$
• D. $\left(\frac{2{\mu }_0{i}^2}{r}\right)$

Answer 1

Answer: (A)

$\left(\frac{{\mu }_0{i}^2}{4r}\right)$

Given that,

Radius = r

Current =i

We know that,

The magnetic force per unit length on the small element P,

$F=Bil$

$\frac{F}{l}=Bi$

$\frac{F}{l}=\frac{{\mu }_0{i}^2}{4r}$

So, The magnetic force per unit length is $\frac{{\mu }_0{i}^2}{4r}$

Hence, A is correct option.