Question

Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?

Answer 1

Let the third wire W₃ having current i in upward direction be placed x cm from the 10 A current wire.

The magnetic force per unit length on a wire due to a parallel current-carrying wire is given by

\[\frac{F}{l} = \frac{\mu_0 i_1 i_2}{2\pi d}\]

According to the question, wire W₃ experiences no magnetic force.

∴ \[\frac{F}{l} \text{ due to wire }W_1 = \frac{F}{l} \text{ due to wire } W_2\]

\[\Rightarrow \frac{\mu_0 10i}{2\pi x} = \frac{\mu_0 40i}{2\pi(10 - x)}\]
\[ \Rightarrow 10 - x = 4x\]
\[ \Rightarrow x = 2 cm\]

Thus, wire W₃ is placed 2 cm from the 10 A current wire.