# Calculating how magnetic field strength decreases with distance

1. May 18, 2014

### downtownjapan

Hi everyone,

I am trying to calculate the decrease in magnetic field strength over distance, using a formula I found on this thread https://www.physicsforums.com/showthread.php?t=522223

The formula given was 1/r^3, where r is the distance from the source.
The same thread says the formula "gives you the magnetic field in Tesla, if you plug in the current in Ampere, the length in meter"

I want to calculate how the field of an electromagnet decreases 0.5 mm directly above, at a 90 degree angle, the center of the one end of the iron core of the electromagnet (Point A shown in the image below).

BUT I must be doing something very, very wrong following this formula because the numbers I get don't make sense to me. I have clearly made a mistake applying the formula and I am wondering if someone could tell me where I have gone wrong.

I am trying to calculate how a field of 0.005 Tesla will decrease at a distance of 0.0005 meters away.

I have done the following calculation
0.005T/0.0005^3 meters, which gives me the number
0.005/0.0005^3 = 40,000,000
I have assumed the unit of the answer (when calculated correctly!) will be in Tesla.
Setting aside the obvious implausibility of a 40 million Tesla magnetic field, the result is always a higher number than I started with (0.005T), but I am trying to calculate how the field strength decreases.
Obviously I have gone horribly wrong, and I have a feeling I am making a very basic mistake somewhere with either the calculations and/or the understanding of the formula.
If any kind-hearted charitable soul out there wants to tell me how this poor fool has gone wrong, I would be very grateful!

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2. May 18, 2014

### Philip Wood

dtj: I'm sorry that the only help I can give on this question is of a negative sort.

• the $\frac{1}{r^3}$ law does not apply here. It only applies if you are a long way away from a magnet compared with the magnet's length. [Assuming the magnet behaves as a dipole.]

[That's not why your answer was so huge; I'm afraid you were not using the $\frac{1}{r^3}$ law correctly - but it doesn't seem worth sorting this out, since the law doesn't apply anyway!]

• You start with a field of 0.005 T, but you don't say where the field has this value.

• This sort of calculation is generally not easy. I hope someone who knows more will jump in...

3. May 18, 2014

### Meir Achuz

0.5 mm is close enough to the end of the magnet to treat the end like a uniformly charged disk.
The B field on its axis is the same as that of the E field on the end of a uniformly charged disk,
which is given in textbooks.
The surface charge on the disk (in gaussian units) is 4pi M.

4. May 19, 2014

### Philip Wood

And how do we find M? Let's suppose that we have a solenoid much longer than its diameter, with an iron core extending to the ends of the coil itself.

5. May 19, 2014

### Meir Achuz

In Gaussian units, the B field (in gauss) at the end of the magnet equals 2pi M.