Question

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Answer 1

Current flowing in wire A, $I_A = 8.0 A$
Current flowing in wire B, $I_B = 5.0 A$
Distance between the two wires, $r = 4.0 \,cm = 0.04 \,m$
Length of a section of wire A, $L = 10 \,cm = 0.1 \,m$
Force exerted on length L due to the magnetic field is given as:
$F = \frac{μ_0I_AI_BL}{2πr}$
Where, $μ_0$ = Permeability of free space = $4π \times 10^7\, TmA^{-1}$
$F= \frac{4π \times 10^{-7} \times 8 \times 5 \times 0.1}{2π \times0.04 } = 2 \times 10^{-5 }N$
The magnitude of force is $2 × 10^{–5 }N$. This is an attractive force normal to A towards B because the direction of the currents in the wires is the same.