# Magnetic Field of an Infinite Solenoid

• Gogsey
In summary, the magnetic field of an infinite solenoid can be found using Ampere's law and is given by 4(pi)In/c, where n is the total number of wraps of the wire. This field is uniform inside the solenoid and zero outside, as demonstrated by the conservation of magnetic field lines. This can be proven by using an intuitive argument and is similar to proving the magnetic field outside a coaxial cable is zero.

#### 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 separate the expressions?

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.

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?

Gogsey said:
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

## 1. What is an infinite solenoid?

An infinite solenoid is a tightly wound coil of wire with an infinite length but a finite radius. It is typically made of a ferromagnetic material and has a uniform magnetic field along its axis.

## 2. How is the magnetic field of an infinite solenoid calculated?

The magnetic field of an infinite solenoid can be calculated using the formula B = μ₀nI, where B is the magnetic field strength, μ₀ is the permeability of free space, n is the number of turns per unit length of the solenoid, and I is the current flowing through the solenoid.

## 3. What is the direction of the magnetic field inside an infinite solenoid?

The magnetic field inside an infinite solenoid is parallel to the axis of the solenoid and in the same direction as the current flowing through it. This creates a strong and uniform magnetic field within the solenoid.

## 4. Does the magnetic field of an infinite solenoid have any practical applications?

Yes, the magnetic field of an infinite solenoid has various practical applications. It is commonly used in devices such as electromagnets, transformers, and inductors. It is also used in medical imaging technology like MRI machines.

## 5. Can the magnetic field of an infinite solenoid be turned on and off?

Yes, the magnetic field of an infinite solenoid can be turned on and off by controlling the current flowing through it. When the current is turned off, the magnetic field dissipates quickly.