How Do You Calculate the Current in Each Wire When a Charge Moves Between Them?

[yankeekd25]

Homework Statement

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.

Homework Equations

Fb= qvb sin theta
B= u0 I / 2 pi r

The Attempt at a Solution

I know these two equations must be used, but I'm not sure what to do with both wires. Do I need to apply the charge to each of the wires and do something with that?

First, do I find B by doing B= Fb/ qv sin 90. Is this correct so far?

Thanks in advance.

 

[rl.bhat]

Since the currents in the wires are in the same direction, magnetic field at any point between the two wires is the difference of the fields due to each wire.
You have written the expression for the net field B. Now find B1 and B2 at the given point.
Using B = B1 - B2, solve for the current.

 

[yankeekd25]

Since the currents in the wires are in the same direction, magnetic field at any point between the two wires is the difference of the fields due to each wire.
You have written the expression for the net field B. Now find B1 and B2 at the given point.
Using B = B1 - B2, solve for the current.

Does B1 = u0 I / 2 pi r, where r is the distance from the point to wire 1, and B2 is the same, but with r= the distance from the charge to the second wire?

 

[rl.bhat]

Does B1 = u0 I / 2 pi r, where r is the distance from the point to wire 1, and B2 is the same, but with r= the distance from the charge to the second wire?

Yes.

 

[yankeekd25]

Yes.

Thank you very much!