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

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

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

Ans: We are given the following:
Current flowing in wire $A_{1} I_{A}=8.0 \mathrm{~A}$
Current flowing in wire $B, I_{B}=5.0 \mathrm{~A}$
Distance between the two wires, $r=4.0 \mathrm{~cm}=0.04 \mathrm{~m}$
Length of a section of wire $\mathrm{A}_{4} \mathrm{I}=10 \mathrm{~cm}=0.1 \mathrm{~m}$
Force exerted on length I due to the magnetic field could be given as:

$\begin{array}{l} \mathrm{B}=\frac{\mu_{0} 2 I_{\mathrm{A}} \mathrm{I}_{\mathrm{A}} \mathrm{I}}{4 \pi r} \\ \text { Where, } \mu_{0}=\text { Permeability of free space }=4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} \mathrm{~A}^{-1} \\ \Rightarrow \mathrm{B}=\frac{4 \pi \times 10^{-7} \times 2 \times 8 \times 5 \times 0.1}{4 \pi \times 0.04} \\ \Rightarrow \mathrm{B}=2 \times 10^{-5} \mathrm{~N} \end{array}$

The magnitude of force is found to be $2 \times 10^{-5} \mathrm{~N}$ . This is an attractive force that is normal to A towards B because the direction of the currents in the wires are the same.

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