Question

Three infinitely long parallel straight current carrying wires A, B and C are kept at equal distance from each other as shown in the figure . The wire C experiences net force F .The net force on wire C, when the current in wire A is reversed will be

(i) Zero 

(ii) F/2 

(iii) F 

(iv) 2F

Answer 1

Answer is (i) Zero

Let \(F_1\) is force per unit, length between A & C

i.e. \(F_1 = \frac{\mu_0}{2\pi}\frac{2I\times I}{2r}\) 

And \(F_2\) is force per unit, length between B & C

\(F_2=\frac{\mu_0}{2\pi}\frac{I\times I}r\)

Now net force on ‘C’ is per unit length

\(F_1+F_2=\frac{\mu}{2\pi}\frac{I^2}r(1+1)\)

\(=\frac{2\mu_0}{2\pi}\frac{I^2}r\) = F(given)

Now Fig b

\(F'_1\) = Repulsive force between A & C

\(=\frac{\mu_0}{2\pi}\frac{2I^2}{2r}\)

\(F'_2=F_2\) = A reactive force between B & C

\(\therefore\) Net force on 'C' \(F'_1-F'_2=0\)

\(F'_1=F'_2=\frac{\mu}{2\pi}\frac{2I^2}{2r}\)

\(\therefore\) Net Force on ‘C’ is zero.