Question

Two parallel wires $1 \, m$ apart carry currents of $1 \, A$ and $3 \, A$ respectively in opposite directions. The force per unit length acting between these two wires is

• A. $6\times10^{-7}\,Nm^{-1} \,$ repulsive
• B. $6\times10^{-7}\,Nm^{-1} \,$ attractive
• C. $6\times10^{-5}\,Nm^{-1} \,$ repulsive
• D. $6\times10^{-5}\,Nm^{-1} \,$ attractive

Answer 1

Answer: (A)

Key concept As we know that, force between two parallel current carrying conductors in the same direction attract each other and those carrying currents in the opposite direction repel each other.
Given, $ I_{1}=1 \,A$
$I_{2}=3 A $
$d =1 \,m$
We know that, force per unit length acting between two wires,
$f=\frac{\mu_{0} I_{1} I_{2}}{2 \pi d} $
$f=\frac{2 \times 10^{-7} \times 1 \times 3}{1} $
$f=6 \times 10^{-7} \,Nm ^{-1}$, repulsive