Question

Two parallel wires aligned with y- axis carrying equal currents in opposite directions are placed at $x=+a$ and $x=-a$ in the x-y plane. The net magnetic field at the origin, O is $B_1$ and at a point P (2a, 0, 0) is $B_2$. Then the ratio $B_1:B_2$ is:

• A. 3:1
• B. 1:2
• C. 1:3
• D. 2:1

Answer 1

The correct option is A 3:1

The magnetic field at a distance 'r' from a current carrying current is given by
$B=\frac{{\mu }_{o}i}{2\pi r}$

Now at origin the magnetic field due to both wires will be in the same direction and as they are carrying the same current, magnetic field at origin will be :
$B_1=2\times \frac{{\mu }_{0}I}{2\pi a}=\frac{{\mu }_{0}I}{\pi a}$
The magnetic field at (2a,0,0) will be :
$B_2=\frac{{\mu }_{0}I}{2\pi a}-\frac{{\mu }_{0}I}{6\pi a}=\frac{{\mu }_{0}I}{3\pi a}$
$\therefore \frac{B_1}{B_2}=\frac{3}{1}$