Eq. for displacement of current-carrying wire due to magnet

[WK95]

1. Homework Statement

This is for a physics lab I am working on. A flowing current causes the wire to deflect towards the right a certain amount that varies depending on the current strength.

I need to derive the equation d=(L/mg)F
where
-- L is the distance between contact 1 and 2 both of which lie in the same vertical line.
-- mg is the weight attached at the end of the wire.
-- F is the strength of the magnetic field.
-- d is the horizontal displacement of the wire at the magnet

The magnets are located in the center of the setup and the vertical distance from contact 1 to the magnet can be approximated to be L/2

For the full lab, see http://skipper.physics.sunysb.edu/~physlab/phy134Lab5Magnetic_Force_v4.pdf

Homework Equations

Derive: d = (L/mg)F
F = 2*F_W *sin(theta)
theta = d/L/2 = 2d/L
See below for the derivations of the second two equations.

The Attempt at a Solution

Here is a free-body diagram of the wire at the point where a magnetic field moves it to the right. Equation (1) is for theta, the angle that F_W makes with the vertical.

I got the equation for theta as follows. Tan(theta) = Opposite/Adjacent. Taking theta to be the angle of the wire to the horizontal, opposite is equation to d and adjacent is taken to be L/2 so this will be the triangle formed by the top half of the wire and the magnet. Thus tan(theta)=d/L/2=2d/L

So I've gotten close but the 4 shouldn't be there. I know I have an error somewhere and likely, the 2s of the equations before should have canceled each other once I combined them.

 

[Aceix]

I also got the same eqn as yours. Check the questiin again

 

[WK95]

Bump.