Two long conductors,separated by a distance d | vedclass

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Question

(C) 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

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) The force per unit length between two parallel conductors carrying currents $I_1$ and $I_2$ separated by distance $d$ is given by $F = \frac{\mu_0 I_1 I_2}{2 \pi d}$.Since the currents are in the same direction,the force is attractive. Let the initial force be $F = k \frac{I_1 I_2}{d}$,where $k = \frac{\mu_0}{2 \pi}$.In the new scenario,the current in one conductor becomes $2I_1$ (or $2I_2$) and the direction is reversed,making the force repulsive (negative sign).The new distance is $d' = 3d$.The new force $F'$ is given by $F' = -k \frac{(2I_1) I_2}{3d} = -\frac{2}{3} \left( k \frac{I_1 I_2}{d} \right) = -\frac{2}{3} F$.

Process	Condition
$(I)$ Adiabatic	$(A)$ $\Delta W = 0$
$(II)$ Isothermal	$(B)$ $\Delta Q = 0$
$(III)$ Isochoric	$(C)$ $\Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D)$ $\Delta U = 0$

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