Magnetic Field at the midpoint between two current carrying coils

[RichardEpic]

Homework Statement

Two identical coils are parallel to each other on the same axis. They are separated by a distance equal to their radius R. They each have N turns and carry equal currents I in the same direction.

Find an expression for the magnetic field strength at the midpoint between the loops.
Express your answer in terms of the variables R, N, I, and appropriate constants.

Homework Equations

B = μIN/l

The Attempt at a Solution

I know the above equation for the magnetic field inside of a solenoid, but I have no idea how to find the dissipated magnetic field 1/2 R away from the solenoid.

Since there are two identical solenoids facing the same direction, I'm assuming the magnetic field will be double the dissipated magnetic field of one of the solenoids 1/2 R away from the coils.

Any formulas or direction on what to do to obtain the dissipated magnetic formula will be appreciated!

 

[Simon Bridge]

You could use Ampere's Law to compute the general equation for the magnetic field along the axis of a finite solenoid (or look it up online)?

Sketching the field-lines on a scale diagram will help you see what to expect.
Do that first.

 

[RichardEpic]

Thank you! I looked up the general equation for the magnetic field along the axis of a finite solenoid, and found something:

http://www.netdenizen.com/emagnet/solenoids/solenoidonaxis.htm

However, it seems I must know the inner radius...I will assume it is zero and see what happens. I also need to know the length of the solenoid, and I have no idea what that is. maybe I'll assume 1..?

 

[RichardEpic]

The answer is apparently:

B =(0.8)^(1.5)*(u*N*I/R)

Could you please explain to me how this comes to be the conclusion...? I'd at least like to understand this problem... :(

 

[Simon Bridge]

Is putting r1=0 (the inner radius) a reasonable thing to do in light of your course so far?
What happens if r1=r2? What would that mean? (Missing out the length is a bit odd - since even for the infinite coil approximation you need the coil density n=N/L.)

Superposition works both ways:
If you had a solenoid radius R length 2L+R - then removed a length R section from the middle, what would that do the the B field there?

Another way to understand your results if you try it for a single loop - then add another loop slightly further away, and again and again ... see how the field adds up.