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Question

(D) The currents are in opposite directions,so their magnetic fields at the mid-point are in the same direction.Both wires are at a distance $r = 1.5

Vedclass · Accepted Answer

$\frac{5 \mu_{0}}{2 \pi}$

Vedclass · Answer

(D) The currents are in opposite directions,so their magnetic fields at the mid-point are in the same direction.Both wires are at a distance $r = 1.5 \,m$ from the mid-point.The magnetic field due to the first wire is $B_{1} = \frac{\mu_{0} I_{1}}{2 \pi r} = \frac{\mu_{0}}{2 \pi} \cdot \frac{3}{1.5} = \frac{2 \mu_{0}}{2 \pi}$.The magnetic field due to the second wire is $B_{2} = \frac{\mu_{0} I_{2}}{2 \pi r} = \frac{\mu_{0}}{2 \pi} \cdot \frac{4.5}{1.5} = \frac{3 \mu_{0}}{2 \pi}$.Since the fields are in the same direction,the resultant magnetic field is $B = B_{1} + B_{2} = \frac{2 \mu_{0}}{2 \pi} + \frac{3 \mu_{0}}{2 \pi} = \frac{5 \mu_{0}}{2 \pi}$.

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