Magnetic Field of an Infinite Solenoid

[Gogsey]

The question is basically asking you to find an expression for the magnetic field of an infinite soleniod, through the center of the solenoid(lengthways), and around the coils of the soleniod.

I know, with help from te textbook, that the magnetic field of a loop is 2(pi)b^2I/cr^3. Where b is the radius of the loop, and R is the distance to a point on the z-axis from the edge of the loop.

And at the centre of the look, z=0, we have 2(pi)I/cb.

Now, we also have that the infinite soleniod magnetic field is 4(pi)In/c, where n is the total number of wraps if the wire.

Is this expression for in the direction of the wraps(around its centre), for the length of the cylindrical soleniod, in that direction, or both? If it is both, how would you seperate the expressions?

[Tom Mattson]

I don't really understand your last question, but an ideal infinite solenoid has a uniform magnetic field inside and a zero magnetic field outside. All you have to to is apply Ampere's law to the problem. You can undoubtedly find the solution on the internet. In fact it's typically worked out in the text of most freshman physics books.

[Gogsey]

The question asks " what is the magnetic field in and around the solenoid".

I think I misread the question. I though around meant the surface of the solenoid/inside the the wire. My bad.

So I guess there's a way to prove that its zero outside the solenoid. Is this similar to proving the magnetic field outside a coaxial cable is zero?

[Tom Mattson]

The question asks " what is the magnetic field in and around the solenoid".

I think I misread the question. I though around meant the surface of the solenoid/inside the the wire. My bad.


Yeah, I'm pretty sure they mean "inside and outside the solenoid".


So I guess there's a way to prove that its zero outside the solenoid. Is this similar to proving the magnetic field outside a coaxial cable is zero?

Here's a nice explanation from Wikipeida:


An intuitive argument can be used to show that the field outside the solenoid is actually zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can. The magnetic field lines go up the inside of the solenoid, so they must go down the outside so that they can form a loop. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced. Recall also that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer.


http://en.wikipedia.org/wiki/Solenoid