Question

When two long parallel wires carry unequal currents, the magnitude of the magnetic force that one wire exerts on the other is F. If the current in both wires is now doubled, what is the magnitude of the new magnetic force on each wire?

Answer 1

Answer:

The magnitude of the new magnetic force on each wire will be 4 times of the initial force.    

Explanation:

When two long parallel wires carry unequal currents, the magnetic force acting on two wires per unit of length is given by :

$\dfrac{F}{l}=\dfrac{\mu_o I_1I_2}{2\pi r}$

r is distance from wires

If the current in both wires is now doubled, new force per unit length is given by :

$(\dfrac{F}{l})'=\dfrac{\mu_o (2I_1)(2I_2)}{2\pi r}\\\\(\dfrac{F}{l})'=4\times \dfrac{\mu_o I_1I_2}{2\pi r}\\\\(\dfrac{F}{l})'=4\times \dfrac{F}{l}$

So, the magnitude of the new magnetic force on each wire will be 4 times of the initial force.