# Magnetic Field and Force (in a solenoid)

1. Feb 26, 2012

### physgrl

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

A 200-turn solenoid is 20.0 cm long and carries a current of 3.25 A. Find the magnetic field. Find the force exerted on a 15.0 µC charged particle moving at 1050 m/s through the interior of the solenoid, at an angle of 11.5° relative to the solenoid’s axis.

2. Relevant equations

r=mv/qB
torque=IABn (n=turns)
B=(μo/2π)*I/r
F=ILBsin(θ)
F=qvBsin(θ)

3. The attempt at a solution

n=200
l=.2m
I=3.25A

If I want to use torque=IABn to find B I need torque and I do not know how to find it with the length only. The second part I understand once I find the Magnetic Field, but I dont get how to find it with the info given.

the answer key says: B=4.08 x 10-3 T and F=1.28 x 10-5 N

2. Feb 26, 2012

### I like Serena

Hi!

I think you need an extra formula.
The magnetic field inside a long solenoid is given by:
$$B=\mu_0 {n I \over \mathcal{l}}$$
as you can see on wiki: http://en.wikipedia.org/wiki/Solenoid

3. Feb 26, 2012

Thanks!