Conceptual? question of direction/magnetic force of current in x-y plane

[rfig08d]

Homework Statement

3 long wires are perpendicular

Each passes through x-y plane with a distance of L from origin. Each wire has a current, I, directed out of the drawing's plane. An electron is located a the origin with a velocity along the positive x-axis. What is the direction of the magnetic force on the electron?

Homework Equations

From what I know F = (4pix10^-7)I/(2*pi*r)

The Attempt at a Solution

I'm at a loss for this... but my thoughts on this are: Would each current (I1, I2, I3) have a negative charge and repel the electron out of the plane towards the negative x-axis?

The answer states that it is "out of the page (ie: graph)" and my understanding makes sense, correct?

 

[collinsmark]

From what I know F = (4pix10^-7)I/(2*pi*r)

Nooo, that's the magnetic field strength, not the force!

For a straight, long wire (not within in a magnetic material),

B = μ₀I/(2πr)​

Use the right-hand rule to find the direction of the vector B.

Then use the Lorenz force equation (with E = 0) to find the force (which also might involve using the right-hand-rule).

The Attempt at a Solution

I'm at a loss for this... but my thoughts on this are: Would each current (I1, I2, I3) have a negative charge and repel the electron out of the plane towards the negative x-axis?

No, there is no net charge on the wire*. For every negative electron in the wire, there is also a positive proton in the wire. The net charge, and thus net electric field, is zero. For this problem you need to deal with magnetic fields, not electric fields.

*I'm intentionally leaving concepts of special relativity out of this conversation. they're not necessary to solve this problem

The answer states that it is "out of the page (ie: graph)"

Yes, out of the page is correct (not toward the negative x-axis). Out of the page meaning toward the positive z-axis.