# Homework Help: Magnetic field in a multi-layered solenoid

1. Jan 28, 2015

### maximus123

Hello everyone, this is probably a simpler problem than I think but here it is
My argument is that the length of the solenoid is the number of turns times the diameter of the wire so

$B=\mu_{0}\times n\times I\\\\ =\mu_{0}\times \frac{N}{L}\times I\\\\ =\mu_{0}\times \frac{N}{N\times d}\times I\\\\ =\mu_{0}\times \frac{1}{d}\times I\\\\ B=4\pi\times 10^{-7}\times\frac{1}{300\times 10^{-6}}\times 10 = 0.042\textrm{ T}$
So one layer gives 0.042 Tesla so to get 10 Tesla you'd need $10/0.042\approx 238$ layers.

I don't have a great deal of confidence in this argument but I'm struggling to see how else to approach this question. Any help would be greatly appreciated. Thanks.

2. Jan 28, 2015

### Staff: Mentor

1 Tesla, not 10.
Looks good.

3. Jan 28, 2015

### maximus123

Ah yes, silly mistake, so 23.8 layers, i.e 24 layers.