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  4. Two long conductors, separated by a distance d carry current I1 and I2 in the same direction. They exert a force F on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to 3d. The new value of the force between them is

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Q. 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 increased to two times and its direction reversed. The distance is also increased to $3d$. The new value of the force between them is

AIEEEAIEEE 2004Moving Charges and Magnetism

Solution:

Force between two long conductor carrying current
$F = \frac{\mu_{0}}{2\pi} \frac{I_{1}I_{2}}{d}\ell$
According to question
$F' = \frac{\mu _{0}}{2\pi } \frac{\left(-2I_{1}\right)I_{2}}{d}\ell$
From equation $\left(i\right)$ and $\left(ii\right)$, $F' = -\frac{3}{2}F.$