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

In summary, the conversation discusses a question about finding the magnitude of the net magnetic field at a specific point between two circular coaxial coils. The formula used in the attempt at a solution is incorrect, and after consulting a reference source, the correct formula is found. The conversation ends with an apology for bothering the expert.
  • #1
phyzmatix
313
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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



[tex]B(z)= \frac{\mu_0}{2 \pi} \frac{\mu}{z^3}[/tex]

The Attempt at a Solution



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

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

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

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

[tex]\mbox{Force at P}=9.84 \times 10^{-5}[/tex]

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
 
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  • #2
Hi phyzmatix! :smile:

(Thanks for the PM.)

I get very confused about currents in coils.

Is the area relevant? :confused:

Anyway, there's a formula at http://en.wikipedia.org/wiki/Helmholtz_coil which … erm … looks nothing like yours! :redface:
 
  • #3
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 :redface:

Sorry to have bothered you :redface:
 

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

What is the purpose of a Helmholtz coil?

A Helmholtz coil is a scientific instrument used to generate a uniform magnetic field for various experiments and measurements.

How is the magnitude of a Helmholtz coil determined?

The magnitude of a Helmholtz coil is determined by the number of turns in the coil, the radius of the coil, and the current passing through the coil.

Can the magnitude of a Helmholtz coil be adjusted?

Yes, the magnitude of a Helmholtz coil can be adjusted by varying the current passing through the coil or by changing the distance between the coils.

What is the ideal distance between the coils for a Helmholtz coil?

The ideal distance between the coils for a Helmholtz coil is equal to the radius of the coils.

How is the magnetic field strength measured in a Helmholtz coil?

The magnetic field strength in a Helmholtz coil is measured using a Gaussmeter, which measures the strength of the magnetic field in Gauss or Tesla.

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