Two long, straight wires are parallel and 25 cm apart.

(a) If each wire carries a current of 50 A in the same direction, what is the magnetic force per meter exerted on each wire? (b) Does the force pull the wires together or push them apart?
(c) What happens if the currents flow in opposite directions?

The magnetic force exerted on each wire is .

The forces on the wires can be calculated by the equation;

Where,

I1 and I2 are the two equal, parrallel currents = 50 A  

r - distance that separates both parallel currents = 25cm = 0.25m  

μo - permeability of free space =  

Put the values in the equation,

Therefore, the magnetic force exerted on each wire is .

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A) 2 x 10^(-3) N/m

B) The force pulls the wires together.

C) If the currents flow in opposite directions, the magnetic force between both wires will be repulsive and it will push both wires apart.

Explanation:

A) The forces on the wires of the two carrying current are equal in magnitude and the force per unit length (F/L) is given by the equation;

F/L = [(μo)(I1)(I2)]/2πr = (μo)(I²)]/2πr

Where I1 and I2 are the two parrallel currents and in this case are equal to 50A

r is the distance that separates both parallel currents = 25cm = 0.25m

μo is the proportional constant called the permeability of free space and it has a value of 4π x10^(-7) N/A²

Thus, plugging in relevant values, we obtain;

F/L = [(μo)(I²)]/2πr

F/L = (4π x10^(-7) x 50²)/(2 x π x 0.25) = 2 x 10^(-3) N/m

B) Normally, we say that the force is attractive if the currents are in the same direction but repulsive if they are in opposite directions. However, in this question, the 2 currents are in the same direction and thus we can say that the force pulls the wires together.

C) If the currents flow in opposite directions, the magnetic force between both wires will be repulsive and it will push both wires apart.

magnitude and direction

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.