Question 291: Magnetism and Matter

Question

Two long parallel wires carrying currents 8A and 15A 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 _____________ $$	imes~10^{-6}$$ T.
(Given : $$\sqrt2=1.4$$)

Accepted Answer

Magnetic fields due to both wires will be perpendicular to each other.
$$
\begin{aligned}
& B_1=\frac{\mu_0 i_1}{2 \pi d} \quad B_2=\frac{\mu_0 i_2}{2 \pi d} \\
& B_{	ext {net }}=\sqrt{B_1^2+B_2^2} = \frac{\mu_0}{2 \pi d} \sqrt{i_1^2+i_2^2} \\
& = \frac{4 \pi 	imes 10^{-7}}{2 \pi 	imes(7 / \sqrt{2}) 	imes 10^{-2}} 	imes \sqrt{15^2+8^2}\left(	ext {As }d=\frac{7}{\sqrt{2}} \mathrm{~cm}ight) \\
& = 68 	imes 10^{-6} \mathrm{~T}
\end{aligned}
$$

Magnetism and Matter

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