First slide

Force on a current carrying wire placed in a magnetic field

Question

Two parallel wires carrying equal currents in opposite directions are placed at x = ±a parallel to y-axis with z = 0. Magnetic field at origin O is $B_{1}$ and at P (2a, 0, 0) is $B_{2}$ . Then, the ratio $\frac{B_{1}}{B_{2}}$ is

Easy

A

3
B

1/2
C

1/3
D

2

Solution

$B_{1} = \frac{μ_{0} i}{2 π a} + \frac{μ_{0} i}{2 π a} = \frac{μ_{0} i}{π a} B_{2} = \frac{μ_{0} i}{2 π . 3 a} - \frac{μ_{0} i}{2 π a} = \frac{μ_{0} i}{3 π a}$

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