Two long, parallel wires are separated by a distance of 3.20 cm. the force per unit length that each wire exerts on the other is 3.30×10−5 n/m, and the wires repel each other. the current in one wire is 0.560 a.
a. what is the current in the second wire?
b. are the two currents in the same direction or in the opposite direction?

(a)The current in the second wire = 9.43 A

(b) The two current are in the opposite direction.

Explanation:

The force per unit length (F/l) on a current carrying conductor = μ₀I₁I₂/2πr

Making I₂ The subject of the equation,

I₂ = [2πr(F/l)]/μ₀I₁ Equation 1

Where I₁ = Current in the first wire, I₂ = current in the second wire, μ₀ = permeability of vacuum, r = distance of separation between the two wires.

Given: F/l = 3.30 × 10⁻⁵ N/m, I₁ = 0.56 A, r = 3.20 cm = 0.032 m.

Constant: μ₀= 4π × 10⁻⁷ Am⁻¹.

Substituting these values into equation 1

I₂ = (2π × 0.032 × 3.30 × 10⁻⁵ )/(4π × 10⁻⁷×0.56)

I₂ = (0.032 × 3.3 × 100)/1.12

I₂ = 10.56/1.12

I₂ = 9.43 A

Therefore the current in the second wire = 9.43 A

(b) The two current are in the opposite direction, because the force on each wire repel each other.

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.