Two parallel long wires carry currents i 1 and i 2 with i 1 i 2 . When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 μ T and when the direction

Question

Two parallel long wires carry currents i 1 and i 2 with i 1 > i 2 . When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 μ T and when the direction of i 2 is reversed, the field becomes 30 μ T . The ratio i 1 i 2 is

TestHub · Accepted Answer

When currents are in the same direction,

$\vec{B_{1}}$ is into the plane and $\vec{B_{2}}$ is up the plane at point $P$ .

$10 = B_{1} - B_{2}$ ......(1)

When the direction is reversed,

Both $\vec{B_{1}}$ and $\vec{B_{2}}$ are into the plane.

$30 = B_{1} - B_{2}$ ......(2)

From (1) and (2)

$B_{1} = 20 T$ and $B_{2} = 10 T$

$∴ \frac{B_{1}}{B_{2}} = \frac{20}{10}$

$∴ \frac{i_{1}}{i_{2}} = \frac{2}{1}$

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