Two long conductors, separated by a distance d, carry...

Two long conductors, separated by a distance $d$, carry current $I_{1}$ and $I_{2}$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is doubles and its direction is reversed. The distance is also increased to $3 d$. The new value of the force between them is (A) $-\frac{2 F}{3}$ (B) $\frac{F}{3}$ (C) $-2 F$ (D) $-\frac{F}{3}$

Two long conductors, separated by a distance $d$, carry current $I_{1}$ and $I_{2}$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is doubles and its direction is reversed. The distance is also increased to $3 d$. The new value of the force between them is
(A) $-\frac{2 F}{3}$
(B) $\frac{F}{3}$
(C) $-2 F$
(D) $-\frac{F}{3}$

Key Concepts

Scaling of Forces Due to Changes in Current and Separation

Any modification in the magnitude of the currents or the separation between the conductors leads to a proportional change in the force. For instance, doubling one current will double the force, while increasing the separation decreases the force because of its inverse relationship with distance. These scaling rules allow predictions of force changes when system parameters are altered.

Magnetic Force Between Parallel Currents

Ampere's force law describes the magnetic force per unit length between two long, parallel current-carrying conductors. This force is directly proportional to the product of the magnitudes of the currents and inversely proportional to the distance between the conductors, with the proportionality constant being expressed in terms of the magnetic permeability of free space.

Effect of Current Direction on Magnetic Interaction

The direction of the currents determines whether the force is attractive or repulsive. When the currents flow in the same direction, they attract each other, and when they flow in opposite directions, they repel. Thus, reversing the direction of one current changes the nature (and sign) of the force between the conductors.

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