Cant uderstand certain parts this

[nabliat]

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


i can't understand certain things in here:
i can't understand the 3d picture.
why the magnetic field in the z direction??

i can't 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??

 

[mighty2000]

Hello,

Thank you for your question. I will try to explain the 3D picture and the calculation of mutual inductance in more detail.

The 3D picture is showing a cross-section view of two solenoids (coils) with current flowing in opposite directions. The magnetic field lines are shown in blue and red, indicating the direction of the magnetic field. The z-direction is simply a reference axis used to define the direction of the magnetic field lines.

Now, for the calculation of mutual inductance, we need to understand the concept of mutual inductance first. Mutual inductance is a measure of how much one coil induces voltage in another coil when the current in the first coil changes. In other words, it is a measure of the coupling between two coils.

The formula you mentioned, M_{12}=\frac{N_2\phi _{12}}{I_1}, is the correct formula for mutual inductance, where N is the number of turns in the second coil and \phi_{12} is the magnetic flux through the second coil due to the current in the first coil.

In this particular situation, we are trying to find the mutual inductance between the two solenoids. To do this, we need to calculate the magnetic flux through one solenoid due to the current in the other solenoid. This is where the EMF (electromotive force) comes in. The EMF is the voltage induced in a coil when the magnetic flux through the coil changes. In this case, the EMF induced in one solenoid due to the current in the other solenoid is equal to the mutual inductance multiplied by the rate of change of current in the second solenoid.

So, by finding the EMF in one solenoid, we can calculate the mutual inductance between the two solenoids using the formula M_{12}=\frac{EMF}{rate of change of current}. This is why the solution shows the EMF first and then calculates the mutual inductance using this formula.

I hope this explanation helps to clarify things for you. Let me know if you have any other questions.