Two infinitely long wires are separated by a distance of d = 1.4 meters. Both have current running in the positive y direction. A charge of q = +2.7 micro-Coulombs is moving in the positive y direction at v = 3.1 E 6 m/s a distance of r = 0.22 meters from the wire on the left as shown in the diagram. The net force from both wires on the charge is in the x direction with a magnitude of 53 E -6 Newtons. What is the current in each wire in amps?

Two vertical wires. A charge q is .22 meters from the left wire. The Velocity vector is in the positive y direction, and the Fb vector is in the negative x direction, perpendicular to the velocity vector. The second vertical wire is 1.4 meters away from the first.

To find the current in each wire, we can use Ampere's Law. Ampere's Law states that the magnetic field created by a current-carrying wire is proportional to the current and inversely proportional to the distance from the wire.

First, let's find the magnetic field created by each wire at the position of the charge:

1. Calculate the magnetic field due to the wire on the left:
- Use the formula for the magnetic field created by a straight wire, given by: B = (μ₀ * I) / (2π * r)
- Where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is the current in the wire, and r is the distance from the wire.
- Plug in the given values: r = 0.22 meters and the distance between the wires (d) = 1.4 meters.
- Let's assume the current in the wire on the left is I₁.
- So, the magnetic field due to the wire on the left is B₁ = (μ₀ * I₁) / (2π * r).

2. Calculate the magnetic field due to the wire on the right:
- Since the wires are infinitely long and parallel, they create the same magnetic field at the same distance from their respective wires.
- Therefore, the magnetic field at the position of the charge due to the wire on the right is also B₁.

Next, let's find the net magnetic field at the position of the charge:

3. The net magnetic field at the position of the charge is the sum of the magnetic fields created by the wires on the left and right:
- B_net = B₁ + B₁ = 2 * B₁.

Now, let's find the current in each wire by using the force experienced by the charge:

4. Use the formula for the magnetic force on a moving charge, given by: F = |q| * |v| * B
- Where F is the force, |q| is the magnitude of the charge, |v| is the magnitude of velocity, and B is the magnetic field.
- Plug in the given values: |q| = 2.7 × 10⁻⁶ C, |v| = 3.1 × 10⁶ m/s, and F = 53 × 10⁻⁶ N.
- Substitute the expression for the magnetic field, B = 2 * B₁, into the formula: F = |q| * |v| * (2 * B₁).

5. Solve the equation for I₁:
- We know that the force experienced by the charge is in the negative x direction, perpendicular to the velocity vector.
- The magnitude of the force can be written as: F = m * a, where m is the mass of the charge and a is the acceleration.
- Since the charge is moving at a constant velocity, we have: a = 0, and thus, F = 0.
- Set the equation F = 0 and solve for I₁.

By solving for I₁, we can find the current in each wire.