Question

Two long, parallel wires carry currents of different magnitudes. if the amount of current in each wire is doubled, what happens to the magnitude of the force between the wires

Answer 1

The force per unit of length between two wires carrying current is
$\frac{F}{L}= \frac{\mu_0 I_1 I_2}{2 \pi r}$
where I1 and I2 are the currents in the two wires, while r is the distance between them.

We can see from the formula that the force is proportional to the product between I1 and I2: $F \sim I_1 I_2$
so, if we double both I1 and I2, we get a factor 4:
$F' \sim (2I_1 )(2I_2)=4 I_1 I_2 =4 F$
so, the force between the wires will be 4 times the original value.