Physics - Magnetism Question with Solution | TestHub

Magnitude of the magnetic field at a particular distance$x$from infinite long wire is given by

$B=\frac{{\mu }_{0}I}{2\pi x}$

For wire$AB,$$B_1=\frac{20{\mu }_0}{2\pi x}\widehat{k}$.......(i)

Due to$BC$

$B_2=\frac{{\mu }_{0}I}{2\pi x}(-\widehat{k})$......(ii)

Due to$DC$

$B_3=\frac{8{\mu }_0}{2\pi x}(-\widehat{k})$......(iii)

Due to$AD$

$B_4=\frac{10{\mu }_0}{2\pi x}(-\widehat{k})$......(iv)

From Equations, (i), (ii), (iii) and (iv)

$B_1+B_2+B_3+B_4=0$[From question]

$\Rightarrow \frac{20{\mu }_0}{2\pi x}-\frac{{\mu }_{0}I}{2\pi x}=\frac{8{\mu }_0}{2\pi x}+\frac{10{\mu }_0}{2\pi x}$

$\Rightarrow 20-I=8+10$

$\Rightarrow I=20-18$

$\Rightarrow I=+2 \mathrm{A}$

(Positive sign shows the direction of current is same direction as that of given direction)