B field of cylinder with time-varying current

[asdf12312]

Homework Statement

In the picture in the figure, three coils are tightly wrapped around a non-magnetic cylinder of diameter Dcyl. Each coil is defined through the diameter of each wire comprising the coil, dcoil1-dcoil3, the current going through each coil, I1-I3, and the number of turns in each coil, N1 – N3. In addition, each coil extends a length equal to a 1/3 the length of the cylinder. Write a program that defines the magnetic field in the centerline of the cylinder (on the z axis) and plots it against z (from –l to l, where l is the length of the cylinder). Note that the cylinder extends from –l/2 to l/2.

The difference in this problem is that I1, I2, and I3 are now time varying (sinusoidal), with magnitudes I1m, I2m, and I3m and frequency w.

The program outputs a graph of Bz and Ez vs t and z from –l to l for:
1. All coils identical – same current I, same diameter, same number of coils. This should give you an answer identical to the case of one coil with current I and number of coils equal to 3N.

Homework Equations

B=B0 * cos(wt) ?
B field of solenoid (constant field) = uNI/L

The Attempt at a Solution

not really sure about the equation for B or E. i know if I is sinusoidal then B must be too. I think it is something like B0*cos(wt), from what I understand in my book.

 

[rude man]

As before, the problem gives redundant information. Since it gives the extent of each coil (l/3) and the number of turns for each coil, the diameter of the wire is redundant and should be omitted from the problem.
If you figured out the problem for dc then substituting an ac current is a gimme.

 

[asdf12312]

I guess I'm just confused how to find Bz and Et. I think I=I1m*cos(wt) but how do i find the E and B field from this?

 

[asdf12312]

Should I just use the solenoid equations? Bz=u*I/(2*pi*r) but since I has time dependence too, would I use just I am (magnitude) instead of the cos(wt)? I guess I would convert Bz then to Et but it would be without the the z in equation.

 

[rude man]

Should I just use the solenoid equations? Bz=u*I/(2*pi*r) but since I has time dependence too, would I use just I am (magnitude) instead of the cos(wt)? I guess I would convert Bz then to Et but it would be without the the z in equation.

Where did you get B_z=u*I/(2*pi*r)? That's the solenoid equation? You previously had the right equation for B inside the solenoid in post 1.
The B field with current = I₀cos(wt) is a gimme.
For the E field, use Faraday's law around a circular path concentric with the solenoid.
Please define Et. Is it a space movie? I think you mean E_z?

 

[asdf12312]

I get B(t)=u*N*I₀*sin(wt)/L, but I was wondering if this is wrong because it should be Bz. also I think it meant E(t) because we need to plot it against t.

 

[rude man]

I get B(t)=u*N*I₀*sin(wt)/L, but I was wondering if this is wrong because it should be Bz. also I think it meant E(t) because we need to plot it against t.

What do you mean by Bz? I thought B_z, i.e. the B field along the z axis which is the solenoid's axis. B = B_z(z,t) in other words it varies with time t and it varies with location along the z axis, and is directed along the z axis.

E = E_θ(z,t), meaning E has mainly a theta component and is also a function of t and z.