Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines join

Question

Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is ______ × 10 - 6 T . (Given: 2 = 1 . 4 )

TestHub · Accepted Answer

Here, the magnetic fields produced by the two wires will be perpendicular to one another.

Magnetic field due to wire carrying current $8 A$ is $B_{1} = \frac{μ_{0} i_{1}}{2 π d}$

and magnetic field due to wire carrying current $15 A$ is $B_{2} = \frac{μ_{0} i_{2}}{2 π d}$

The net magnetic field is

$B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}} = \frac{μ_{0}}{2 π d} \sqrt{i_{1}^{2} + i_{2}^{2}}$

$= \frac{4 π \times 10^{- 7}}{2 π \times (\frac{7}{\sqrt{2}}) \times 10^{- 2}} \times \sqrt{8^{2} + 15^{2}} (d = \frac{7}{\sqrt{2}} cm)$

$= 68 \times 10^{- 6} T$ .

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