Question

Two long, parallel wires carry currents of different magnitudes. If the amount of current in one of the wires is doubled, what happens to the magnitude of the force that each wire exerts on the other

Answer 1

The magnitude of the force that each wire exerts on the other will increase by a factor of two.

Step-by-step explanation:

force on parallel current carrying wire, F = BILsinθ

where;

B is the strength of the magnetic field

L is the length of the wire

I is the magnitude of current on the wire

θ is the angle of inclination of the wire

Assuming B, L and θ is constant, then F ∝ I

F = kI

`(F_1)/(I_1) = (F_2)/(I_2)`

When the amount of current is doubled in one of the wires, lets say the second wire;

`(F_1)/(I_1) = (F_2)/(2I_1) \\\\F_2 = (2F_1I_1)/(I_1) \\\\F_2 =2F_1`

Also, if will double the amount of current on the first wire, then

F₁ = 2F₂

Therefore, the magnitude of the force that each wire exerts on the other will increase by a factor of two.