# Self-inductance of an inductor - theoretical vs measurment

1. Dec 8, 2008

### Nick89

Hi,

I did an experiment where one of the 'questions' was to determine the self-inductance of an inductor. I am going to leave out the experimental method, but if you need to know just say so and I'll try to explain.

The value I got was $$L = (3.910 \pm 0.009) \text{ mH}$$.

I am fairly confident that this is correct, because 4 people who did the experiment before me got the same value, and my teachers also confirmed that was the result we are looking for.

Now, I need to compare this value to the value obtained from the theoretical formulas.

I used the following:
$$L = \frac{N \Phi}{i}$$
$$\Phi = BA$$
$$B = \frac{\mu_0 N i }{\ell}$$

So
$$L = \frac{\mu_0 N^2 A}{\ell}$$
(N is the number of turns, A is the cross-sectional area, $$\ell$$ is the length of the inductor and i is the current.

Plugging in the values for A, l, N etc, I get a value of L = 1.79 mH.

I am about a factor 2 off..? How did this happen?

I was wondering if this could be because of the many assumptions (that may not be true here) and approximations for example for the magnetic field of an inductor (which assumes a very long inductor if i remember correctly...)?

Could that really cause such a large error? I doubt it... But if they are correct that would mean 4 people + my teacher measured the inductance wrongly?