Question 59 of 276

Two long current carrying conductors are placed parallel to each other at a distance of $8cm$ between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is $300\mu T$. The equal current flowing in the two conductors is :

A$30A$ in the same direction.B$60A$ in the opposite direction.C$30A$ in the opposite direction.D$300A$ in the opposite direction.

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Answer: (C) $30A$ in the opposite direction.

Magnetic field in parallel wires is given by $B=\dfrac{{\mu }_{0}I}{2\pi d}$
At midway, $\text{distance}=\dfrac{d}{2}$
$∵\dfrac{{\mu }_{0}I}{\dfrac{2\pi d}{2}}\times 2=B$
$\Rightarrow \dfrac{{\mu }_{0}}{\pi }\times \dfrac{2I}{d}=B$
$\Rightarrow \dfrac{4\times {10}^{-7}\times 2I}{0.08}=300\times {10}^{-6}$
$\Rightarrow I=\dfrac{3\times {10}^{-4}\times 0.08}{2\times 4\times {10}^{-7}}=30A$
As ${B}_{net}\neq 0$, so the wires are carrying current in opposite direction.