# Mutual induction coeff question

1. Aug 28, 2009

### nabliat

here is the question and solution:
http://i29.tinypic.com/30cy4cn.jpg

i cant understand certain things in here:
i cant understand the 3d picture.
why the magnetic field in the z direction??

i cant understand how did they find the mutual inductance here.
because by this formula

$$M_{12}=\frac{N_2\phi _{12}}{I_1}$$

in our situation we need to find the current in the celonoid
but they for some weird reason find the emf
and right after without any calculation
they show the mutual induction coeff

why??

2. Aug 28, 2009

### gabbagabbahey

They set up their co-ordinate system so that the z-axis runs parallel to the solenoids axis, that's why the field points in the z-direction.

As for $M$, it comes straight from its definition, together with Faraday's law:

$$\Phi_{\text{loop}}=MI_{\text{solenoid}}\implies \varepsilon_{\text{loop}}=-\frac{d\Phi_{\text{loop}}}{dt}=-M\frac{d I_{\text{solenoid}}}{dt}$$

3. Aug 29, 2009

thank :)