Calculting the length of a solenoid

[Taylor_1989]

Homework Statement

Q2

A Cu wire of circular section and diameter 0.2 mm is used to form a one-turn coil and also to form a solenoid. Both have a radius of 2 cm. In both cases, a 10 mA current flows through the wire.

a)Work out the magnetic field H in the centre of the one-turn circular coil.
b) In the second instance, when the wire was wound 500 times to form the solenoid, work out the magnetic field H and B inside the solenoid, far from the edges.

Homework Equations

The Attempt at a Solution

So I am having a issue with my ans to the mark scheme ans for this question, so my first correct, but when I go to calculate the second part this is where thing go a miss.

The equation I am using for magnetic field intensity is
$$H=\frac{I \cdot N}{L}$$
Now from the question I think L is the length of the conductor, which I believe to be 4cm 2 time the diameter.

But when I got to check my answer, it states that
$$L=N*r=500*0.2mm$$
which is the diameter of the wire, but how is this the length of the solenoid, could someone please explain, or have I miss understood the question or worse the physics?

 

[Doc Al]

Now from the question I think L is the length of the conductor, which I believe to be 4cm 2 time the diameter.

For the field within a solenoid, L is the length of the solenoid. (What matters is the number of turns per length: N/L.)

 

[Taylor_1989]

I am not sure what you mean by number of turns per length, 1000/0.04, how dose this related to the diameter that thye have given, has I can't see how the diameter is playing a role in this.

 

[Doc Al]

I am not sure what you mean by number of turns per length, 1000/0.04, how dose this related to the diameter that thye have given, has I can't see how the diameter is playing a role in this.

Assume that the solenoid is just one layer thick. So the diameter of the wire, and the number of turns, tells you the length of the solenoid.

 

[Taylor_1989]

But is the question not saying that I have a long peace of wire, I then form a circular loop with that wire, which has a radius of 2cm so the actual wire length is 4cm. I mean could then get that same 4cm wire and form 1000 loop with it it still 4cm? This is how I am seeing the question.

 

[Doc Al]

No, treat these as two separate problems. You have a spool of wire and you make a single loop with the given radius. The length of the wire is 2*pi*r, of course.

For the solenoid you'll be making 500 loops, so you'll need more wire. (500 times more!)

 

[Taylor_1989]

AH! okay, thank you, now it make sense, I kept thinking I have a wire of 4cm and that was it, I did think it was strange that it was saying 500 turns but I ignored (which I shouldn’t of).

Once again thank you, I will try to read the question more carefully next time.

 

[Doc Al]

Good!