Q119 / 150 · MHT CET 2022 (10 Aug Shift 2) · Physics

Two parallel conducting wires of equal length are placed distance $d$ apart carry current $I_1$ and $I_2$ respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

  • A
    $\frac{\mu_0\left(I_1-I_2\right)}{2 \pi d}$
  • B
    $\frac{\mu_0\left(I_1+I_2\right)}{2 \pi d}$
  • Correct answer
    C
    $\frac{\mu_0\left(I_1+I_2\right)}{\pi d}$
  • D
    $\frac{\mu_0\left(I_1-I_2\right)}{\pi d}$

Solution

Field due to a current-carrying long wire is given by $B=\frac{\mu_0 I}{2 \pi r}$ The field at the midpoint between the two wires are in the same direction and hence get added. The distance of the midpoint $r=\frac{d}{2}$ $\begin{aligned} & \therefore B=B_1+B_2=\frac{\mu_0 I_1}{2 \pi\left(\frac{d}{2}\right)}+\frac{\mu_0 I_2}{2 \pi\left(\frac{d}{2}\right)} \\ & =\frac{\mu_0\left(I_1+I_2\right)}{2 \pi\left(\frac{d}{2}\right)}\end{aligned}$

Hence, the correct answer is option: 'C'.

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