Three infinite straight wires $\mathrm{A}, \mathrm{B}$ and C carry currents as shown in figure. The…

Three infinite straight wires $\mathrm{A}, \mathrm{B}$ and C carry currents as shown in figure. The resultant force on wire B is directed
  1. towards A
  2. towards C
  3. perpendicular to the plane of page
  4. upwards

Solution

$\mathrm{F}=\mathrm{BIL}$
Magnetic field due to $A: \frac{\mu_0 I}{2 \pi d}=\frac{\mu_o}{2 \pi d}$ Force on $B$ due to $A$, $\mathrm{F}_{\mathrm{AB}}=\frac{\mu_0}{2 \pi \mathrm{~d}} \times \mathrm{I} \times \mathrm{L}$
Magnetic field due to $\mathrm{C}: \frac{\mu_{\mathrm{o}} \mathrm{I}}{2 \pi \mathrm{~d}}=\frac{\mu_{\mathrm{o}} \times 3}{2 \pi \mathrm{~d}}$ Force on B due to C, $\begin{aligned} & \mathrm{F}_{\mathrm{CB}}=\frac{3 \mu_{\mathrm{o}}}{2 \pi \mathrm{~d}} \times \mathrm{I} \times \mathrm{L}\\ \therefore \quad & \mathrm{~F}_{\mathrm{AB}} \lt \mathrm{F}_{\mathrm{CB}} \end{aligned}$ $\therefore \quad$ The resultant force will be towards A

Asked in: MHT CET 2024 (15 May Shift 2)

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