Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7cm 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 _______ $10^{- 7} T .$
(Given : $\sqrt{2} = 1.4$ )

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answer is 680.

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Detailed Solution

Given, $i_{1} = 8 A, i_{2} = 15 A$
Distance between two wire = 7 cm
Question Image

$B_{1} = \frac{μ_{0}}{2 π} \times \frac{8}{3.5 \sqrt{2} \times 10^{- 2}} a n d B_{2} = \frac{μ_{0}}{2 π} \times \frac{15}{3.5 \sqrt{2} \times 10^{- 2}}$

So, $B_{n e t} = \sqrt{B_{1}^{2} + B_{2}^{2}}$

$B_{n e t} = \frac{μ_{0}}{2 π} \times \frac{1}{3.5 \sqrt{2} \times 10^{- 2}} \sqrt{8^{2} + 15^{2}} B_{n e t} = \frac{μ_{0}}{2 π} \times \frac{1}{3.5 \sqrt{2} \times 10^{- 2}} \times 17 B_{n e t} = 680 \times 10^{- 7} T$