Three long, straight parallel wires carrying currents are arranged as shown. The wire C which carries a…

Three long, straight parallel wires carrying currents are arranged as shown. The wire C which carries a current of 5.0 A is so placed that it experiences no force. The distance of wire C from wire D is
  1. 9 cm
  2. 7 cm
  3. 5 cm
  4. 3 cm

Solution

Wire C experiences no force. $\begin{array}{ll} \therefore & \mathrm{F}_{\mathrm{CD}}=\mathrm{F}_{\mathrm{CB}} \\ \therefore & \frac{\mu_0 \mathrm{i}_{\mathrm{C}} \mathrm{i}_{\mathrm{D}}}{2 \pi \mathrm{x}}=\frac{\mu_0 \mathrm{i}_{\mathrm{c}} \mathrm{i}_{\mathrm{B}}}{2 \pi(15-\mathrm{x})} \\ \therefore & \frac{5 \times 15}{\mathrm{x}}=\frac{5 \times 10}{15-\mathrm{x}} \\ \therefore & x=9 \mathrm{~cm} \end{array}$

Asked in: MHT CET 2024 (02 May Shift 2)

Practice more Magnetic Fields due to Electric Current questions on Aicharya