Suppose two conducting wires each of mass 25g and length 40m are both hanging from a support beam. When the circuit is turned on, the wires repel each other so that the angle between the supporting strings is 30 degrees at a height 5cm below the support beam.

A. Are the currents going in the same direction or opposite direction?
B. What is the current going through each wire? (Wires have same current)

To determine the direction of the currents in the wires, we need to consider the repulsion between the wires. Since the wires repel each other, we know that the two currents must be in the same direction. This is because currents moving in the same direction create a magnetic field that causes them to repel each other.

To find the current going through each wire, we can use the equation for the force between two current-carrying wires. The force between the wires can be calculated using the formula:

F = μ₀ * I₁ * I₂ * l / (2 * π * r)

where F is the magnitude of the force, μ₀ is the permeability of free space (a constant), I₁ and I₂ are the currents in the wires, l is the length of the wires, and r is the distance between the wires.

Given that the wires have the same current (I₁ = I₂) and the length of each wire is 40m, we can simplify the equation to:

F = μ₀ * I² * l / (2 * π * r)

The angle between the supporting strings can help us find the distance between the wires (r). Since we know that the height between the wires is 5cm and the angle between the supporting strings is 30 degrees, we can use trigonometry to find r.

First, we need to convert the height to meters: 5cm = 0.05m.

Next, we can use the tangent function:

tan(30°) = 0.05m / r

Simplifying this equation, we find that r = 0.05m / tan(30°).

Now, we have all the information we need to calculate the force (F) between the wires. We can rearrange the equation:

F = μ₀ * I² * l / (2 * π * r)

to solve for I:

I = sqrt((F * (2 * π * r)) / (μ₀ * l))

Substituting the values into the equation, we can calculate the current going through each wire, given that the wires have the same current:

I = sqrt((F * (2 * π * r)) / (μ₀ * l))

Remember to convert the length of the wires to meters (l = 40m).

Once we have calculated the current, we can conclude:

A. The currents in the wires are going in the same direction.
B. The current going through each wire (I₁ = I₂) can be determined using the formulas and calculations outlined above.