Three long straight and parallel wires carrying currents are arranged as shown The wire $\mathrm{C}$ which…

Three long straight and parallel wires carrying currents are arranged as shown The wire $\mathrm{C}$ which carries a current of $50 \mathrm{~A}$ is so placed that it experiences no force. The distance of wire $\mathrm{C}$ from wire $\mathrm{A}$ is
  1. $3 \mathrm{~cm}$
  2. $5 \mathrm{~cm}$
  3. $9 \mathrm{~cm}$
  4. $7 \mathrm{~cm}$

Solution

The correct option is (C). Concept: Using Ampere's circuital law the magnetic field due to a current carrying wire at a distance $r$ is given by, $B=\frac{\mu_0 I}{2 \pi r}$ where, $\mathrm{I}$ is the current through the wire. If the magnetic field due to the wire A cancels out the magnetic field due to the wire $\mathrm{B}$ at the wire $\mathrm{C}$, then $\frac{\mu_0 I_A}{2 \pi x}=\frac{\mu_0 I_B}{2 \pi(15-x)}$ $\frac{(15-x)}{x}=\frac{I_B}{I_A}$ Therefore, for $\mathrm{I}_{\mathrm{B}}=10 \mathrm{~A}$ and $\mathrm{I}_{\mathrm{A}}=15 \mathrm{~A}$, we get $\mathrm{x}=9 \mathrm{~cm}$.

Asked in: MHT CET 2022 (05 Aug Shift 1)

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