## Magnetic Force in a Current Carrying Wire

1. The problem statement, all variables and given/known data

The current in a wire consists of n electrons per unit volume moving with a velocity v. What is the effect on these electrons of the magnetic field set up by the current itself within the wire? What is the force on one electron at a distance r from the centre of the wire?

2. Relevant equations

F = QvBsinθ
Magnetic field strength at a distance r from the axis of the wire outside the wire = u0I/2∏r

3. The attempt at a solution

I know that for part 1, the effect of the magnetic field on the electrons inside the wire will be a radially outward force (taking all electrons to be travelling in straight lines along the wire).

Part 2

F will be equal to QvBsin90 = QvB

Making the subsitution for B I have

F = Qvu0I/2∏r

I believe now that I have to make subsitution for I. Which would be 4/3∏a3vne

where e is fundamental charge and a is the radius of the wire.

This gives:

F = (3/8)u0ve2na3r

I know that the answer is:

F = (1/2)u0v2e2nr
I think I'm making a mistake in calculating my current, but I'm not sure. Help Please?

Thanks

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 Hi! This is my first time helping someone out so here goes: To make the substitution for current I, you should use: $I=\int J \bullet da$ where J is the current density, equal to nev in this case. After doing a quick integration you should get the proper current which will give the correct answer for the force.