How Is the Magnetic Field Calculated at the Midpoint of a Helmholtz Coil?

[phyzmatix]

Homework Statement

The picture shows (there's supposed to be a pic) a Helmholtz coil consisting of two circular coaxial coils, each of 200 turns and radius R = 25.0 cm, separated by a distance s = R. The two coils carry equal currents i = 12.2 mA in the same direction. Find the magnitude of the net magnetic field at point P, midway between the coils.

Homework Equations

$$B(z)= \frac{\mu_0}{2 \pi} \frac{\mu}{z^3}$$

The Attempt at a Solution

I thought this was a pretty straightforward question and did the following:

$$\mu=NiA=(200)(12.2 \times 10^{-3} A)(\pi \times (0.25 m)^2) =4.79 \times 10^{-1} Am^2$$

$$B(z)= (\frac{1.26 \times 10^{-6}H/m}{2 \pi})( \frac{4.79 \times 10^{-1}}{(0.125m)^3})$$
$$=4.918 \times 10^{-5}T$$

Now, the magnetic force from both coils are in the same direction, so I multiplied the above answer with two and got

$$\mbox{Force at P}=9.84 \times 10^{-5}$$

However, this doesn't seem to be correct according to the answers I have...Could you tell me where I went wrong please? I'm clueless.

Thanks!
phyz

 

[tiny-tim]

Hi phyzmatix!

(Thanks for the PM.)

I get very confused about currents in coils.

Is the area relevant?

Anyway, there's a formula at http://en.wikipedia.org/wiki/Helmholtz_coil which … erm … looks nothing like yours!

 

[phyzmatix]

Cheers Tiny-Tim! There are no excuses here...I had that EXACT same page open in front of me last night and didn't notice that the answer was right there...Shows you that skimming too quickly isn't always the best way to approach things

Sorry to have bothered you