Two long conductors,separated by a distance d | vedclass

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Question

(A) The force per unit length between two parallel conductors carrying currents $I_1$ and $I_2$ separated by distance $d$ is given by $F = \frac{\mu_0

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$-\frac{2F}{3}$

Vedclass · Answer

(A) The force per unit length between two parallel conductors carrying currents $I_1$ and $I_2$ separated by distance $d$ is given by $F = \frac{\mu_0 I_1 I_2}{2\pi d}$.According to the problem,the initial force is $F = \frac{\mu_0 I_1 I_2}{2\pi d}$.In the new condition,the current in one conductor becomes $I_1' = -2I_1$ (negative sign indicates reversed direction) and the distance becomes $d' = 3d$.The new force $F'$ is given by:$F' = \frac{\mu_0 (-2I_1) I_2}{2\pi (3d)}$$F' = -\frac{2}{3} \left( \frac{\mu_0 I_1 I_2}{2\pi d} \right)$Substituting the initial force $F$ into the equation:$F' = -\frac{2}{3} F$.

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