# Acceleration of a wire inside a magnetic field

1. Oct 15, 2013

### kopinator

A uniform horizontal wire with a linear mass density of 0.520 g/m carries a 2.70 A current. It is placed in a constant magnetic field, with a strength of 4.17×10-3 T, that is horizontal and perpendicular to the wire. As the wire moves upward starting from rest, what is its acceleration? Neglect the magnetic field of the Earth.

F=ma
F=ILB

From these two equations, I derived an equation a= ILB/m. I have all the variables except L and m which will come with each other once I figure how to incorporate the mass density. So my question is, how do I use the linear mass density in this problem?

2. Oct 15, 2013

### UltrafastPED

m/L is the mass density.

3. Oct 15, 2013

### kopinator

ok. So i rearranged the equation to be ma/L=IB. Since the mass density is .520 g/m, I divided IB/.520 and got .02165 m/s^2. But when i plugged it in it was wrong. I converted .520 g/m to .000520 kg/m and solved and still got the wrong answer. What am I doing wrong?

4. Oct 15, 2013

### UltrafastPED

I get 21.65 N. What is the "correct" answer?

Lay out all of your numbers and calculate again; also what happened to the kg?

5. Oct 15, 2013

### kopinator

I figured it out. 21.65 m/s^2 was the correct value from the equation but I had to take into account that the wire is still being affect by Earth's gravitational acceleration so i took 21.65-9.81 = 11.84 m/s^2. Thank you for ur assistance!

6. Oct 15, 2013

### UltrafastPED

I thought it said " Neglect the magnetic field of the Earth", which is averages 0.5 gauss:
http://en.wikipedia.org/wiki/Earth's_magnetic_field

But if it is to be included we have 1 T = 10,000 gauss, so the it is 0.05 x 10^-3 T, or about 1% of your given field; and of course the force depends upon the direction of the wire ... so assuming that the fields are anti-parallel (opposite polarities) the reduction is only 0.22 N or so.