Question

A conductor $AB$ of length $L$ carrying a current $I^{\prime }$ as shown in figure. The force on $AB$ has magnitude

• A. $\frac{{\mu }_0{I}^{\prime }I}{2\pi }\log 2$
• B. $\frac{{\mu }_0{I}^{\prime }I}{2\pi }\log 3$
• C. $\frac{{3\mu }_0{I}^{\prime }I}{2\pi }\log \frac{3}{2}$
• D. $\frac{{2\mu }_0{I}^{\prime }I}{3\pi }$

Answer 1

The correct option is B $\frac{{\mu }_0{I}^{\prime }I}{2\pi }\log 3$

Consider an element of length $dx$ on $AB$, at a distance $x$ from $XY$.

Force on the element: $dF=\left({\mu }_{0}I/2\pi x\right)I^{\prime }dx$

Total force on $AB$,

$F={\int }_{L/2}^{3L/2}\frac{{\mu }_{0}I{I}^{\prime }}{2\pi x}dxF=\frac{{\mu }_{0}I{I}^{\prime }}{2\pi }\log 3$