In a question:

To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12cm in diameter and 50cm in length. You would like a 2.2 A current to produce a 2.6 kG magnetic field inside your solenoid.

What is the total length of wire you will need to meet these specifications?

In the provided answer:

$$NC = nL C = (\frac{B}{\mu_0 I}) L (\pi d)$$


  • $N$ is total number of turns
  • $n$ is number of loops
  • $C$ is circumference

But I dont understand why is there an $L$

I did it by:

$$B = \mu_0 n I$$

Then length of wire needed is just $nC$ whats wrong?


1 Answer 1


$n$ in this case isn't the number of loops, it's the number of loops per unit length. This is why you have to multiply it by $L$ to get $N$.

  • $\begingroup$ True. Our professor stressed on this point a lot, so that we wouldn't make a mistake. :) $\endgroup$ Jun 25, 2013 at 12:14

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