Question

The force between two parallel current carrying conductors separated by a distance $x$ is $F$. If the current in each conductor is doubled and the distance between them is halved, then the force between them becomes.

• A. $F$
• B. $2F$
• C. $4F$
• D. $8F$

Answer 1

The correct option is D $8F$

Given

Two parallel wires having current i1 and i2

Distance between them is x

Force between them is F

length of two wires is L

Solution

Force between wires is

$F=\frac{{\mu }_0{i}_1\ast i_2\ast L}{2\pi x}$

We can see that

F is directly proportional to product of currents

F is inversely proportional to x

So if we double the currents F will become 4 times

And if we halved the x, F will become 2 times

if we combine F become 8 times

The correct option is D