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 $A.$
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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:
$B=\frac{\mu_{0} 2 I_{A} I_{B} l}{4 \pi r}$
Where,
$\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7} \,T\,m\,A ^{-1}$
$B=\frac{4 \pi \times 10^{-7} \times 2 \times 8 \times 5 \times 0.1}{4 \pi \times 0.04}$
$=2 \times 10^{-5} \;N$
The magnitude of force is $2 \times 10^{-5}\,N$. This is an attractive force normal to A towards B because the direction of the currents in the wires is the same.
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