College Physics-Helmholtz coil?

Question

Here is the link to the problem:

http://i152.photobucket.com/albums/s167/gt_badone/Ch.jpg

Answer 1

It's a very interesting problem, to tell you the truth is the second time I heard about that, but I was trying to remember how to calculate the magnetic field of a Helmholtz coil, then I looked it up in a book, and got it :

B = (4/5)^3/2*N*U0*I / 2*pi*R

R = radius

N = turns

Uo = permeability = 4pi*10^-7

I = current

Now, we are gonna calculate it for one coil, then we just have to multiplicate the result by two, and the direction will be found using the right hand rule.

B1 = (4/3)^3/2*282*4pi*10^-7*8,42*10^3 / 2pi*27.6*10^-2

B1 = (4/3)^3/2*172*10^-2 (Tesla)

B1 = 264.88*10^-2 = 2.65 (Tesla)

This is the electromagnetic field at P, by one of the coils, the other coil will produce the same magnetic field, then, the final resulto will be :

Total B = 5.3 (Tesla)

Using the righ hand rule, the direction will be downwards

To the minus "y"

B = 5.3 -j Tesla