Question

The magnitude F of the force between two straight parallel current carrying conductors kept at a distance d apart in air is given by

\(F=\frac{\mu_0I_1I_2}{2\pi d}\)

Where I₁ and I₂ 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 is assigned a positive sign”. 

Draw graphs showing dependence of F on 

(i) I₁ I₂ when d is kept constant 

(ii) d when the product I₁ I₂ is maintained at a constant positive value. 

(iii) d when the product I₁ I₂ is maintained at a constant negative value.

Answer 1

We know that F is an attractive (–ve) force when the currents I₁ and I₂ are ‘like’ currents i.e. when the product I₁ I₂ is positive.

Similarly F is a repulsive (+ve) force when the currents I₁ and I₂ are ‘unlike’ currents, i.e. when the product I₁ I₂ is negative.

Now F∝ (I₁I₂), when d is kept constant and F∝1/d when I₁I₂ is kept constant. 

The required graphs, therefore, have the forms shown below: