Question

Two long parallel wires carrying currents 2.0 A and 4.0 A respectively in opposite directions. The separation between the wires is 0.25 m. Calculate the force per unit length between them in the order of ${10}^{-6}$.Also, state whether it will be attractive or repulsive.Take magnetic permeability as ${\mu }_0=4\pi \times {10}^{-7}N/A^2$
Formula to be used, $F\left(perunitlength\right)=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$

• A. 6, repulsive
• B. 4.5, attractive
• C. 6, attractive
• D. 4.5, repulsive

Answer 1

The correct option is A 6, repulsive

Given
Current,$I_1=2.0A$
Current,$I_2=4.0A$
Distance,d =0.25 m
permeability,$\left({\mu }_0\right)=4\pi \times {10}^{-7}N/A^2$
Formula to be used, $F=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$
Substituting the given values, $F=6.4\times {10}^{-6}N/m=6\times {10}^{-6}N{m}^{-1}$
Since the currents are in opposite directions, they are anti-parallel and hence have a repulsive force between them.