Solenoid length of wire problem

[kayak4life87]

Hey so I have been trying this problem and just cannot get it. thanks for the help.

To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12cm in diameter and 55cm in length. You would like a 2.0A current to produce 2.5kG magnetic field inside your solenoid. What is the length of wire you will need to meet these specifications? The answer is 21km, but i cannot get this to work

 

[Nick89]

What have you tried so far? You are supposed to show your work first.

A hint: Can you find an expression for the magnetic field in the solenoid? What is the unknown variable in this expression, and can you use that to get the answer?

 

[kayak4life87]

well i have used the B=uo(N/L)I n=N/L I tried solving for n and then plug that into the second equation there and solving for N. Then once you have N put that into the first equation and solve for L. However, this is not working and I don't really know another approach unless I am doing something in the wrong order. thanks.

 

[Nick89]

I don't fully understand what you have done. You start of right! But I don't understand what you mean once you get to solving for N.

Use
$$B = \frac{\mu_0 I N}{L}$$

You know B, I and L. So you can solve for N.
That gives you the total number of turns of wire.

There is one value you haven't used yet, which you need to calculate the length of the wire you need.EDIT
I just noticed, the B-field is given in Gauss. For the expression of the B-field to be correct unit-wise, you need to enter L in meters, I in amperes and $\mu_0$ in $m \, kg \, s^{-2} A^{-2}$. This will yield the magnetic field strength B in Tesla, not Gauss! Note that 1 Gauss = 10^-4 Tesla.

 

[kayak4life87]

ya i converted the 2.5kG to Tesla 1kG=1000Gauss 1Gauss=.0001 tesla

You are given B, I, uo, L=55cm, diameter=12cm, B=2.5kG=0.25T

I first used the equation B=uo(n)I and solved for n, then used n=N/L to solve for N

then once you have N I put that back into B=uo(N/L)I. But of course I am just going in circles and am confused.. sorry for the confusion.

 

[alphysicist]

Hi kayak4life87,

ya i converted the 2.5kG to Tesla 1kG=1000Gauss 1Gauss=.0001 tesla

You are given B, I, uo, L=55cm, diameter=12cm, B=2.5kG=0.25T

I first used the equation B=uo(n)I and solved for n, then used n=N/L to solve for N

then once you have N I put that back into B=uo(N/L)I. But of course I am just going in circles and am confused.. sorry for the confusion.

I think you might have misread Nick89's post. The $L$ in that equation is not the length you are looking for. The $L$ in that equation is the length of the solenoid (for example, perhaps the plastic tube that the wire is wrapped around), but the length you are looking for is the total length of the wire when it is stretched out.

 

[kayak4life87]

aaahhh.. i got it now.. i was not even thinking when that was the length of solenoid. I found the number of turns and then used the circumference of the cylinder.. Thanks everyone for your help. thanks again.