Question: Q. 15. The magnitude $F$ of the force between two straight parallel current carrying conductors kept at a distance $d$ apart in air is given by
$$ F=\frac{\mu_{0}}{2 \pi} \cdot \frac{I_{1} I_{2}}{d} $$
where, $I_{1}$ and $I_{2}$ are the currents flowing through the two wires
Use this expression, and the sign convention that the :
“Force of attraction is assigned a negative sign and force of repulsion assigned a positive sign”.
Draw graphs showing dependence of $F$ on :
(i) $I_{1} I_{2}$ when $d$ kept constant
(ii) when the product $I_{1} I_{2}$ is maintained at a constant positive value.
(iii) when the product $I_{1} I_{2}$ is maintained at a constant negative value.
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Solution:
Ans. We know that $F$ is an attractive (- ve) force when the currents $I_{1}$ and $I_{2}$ are ’like’ currents, i.e., when the product $I_{1} I_{2}$ is positive or when they are flowing in same direction.
Similarly $F$ is a repulsive (+ve) force when the currents $I_{1}$ and $I_{2}$ are ‘unlike’ currents, i.e., when the product $I_{1} I_{2}$ is negative or when they are flowing opposite direction.
Now $F \propto\left(I_{1} I_{2}\right)$, when $d$ is kept constant and $F \propto \frac{1}{d}$ when $I_{1} I_{2}$ is kept constant.
The required graphs, therefore, have the forms shown below.
(i)
(ii)
(iii)
