The field due to multiple concentric solenoids with water

Jeremy_W
Messages
1
Reaction score
0

Homework Statement


OK, so I am doing research this semester and I am working with the Faraday effect. For my magnetic field, we are using a large solenoid that is comprised of 13 concentric solenoids each of which has the same number of coils per unit length. In between each of these layers there are layers of water to cool the wires to prevent overheating and of course in the middle is the substance which the light will pass through. However, for this calculation, I will assume it to be a vacuum (under the instruction of the professor). So I need to calculate the magnetic field strength.

Homework Equations


Ampere's Law: ∫B.ds=μOJ
Magnetic Field of one solenoid with a non-vacuum core: B = μnI

The Attempt at a Solution


Well, I read in another thread that the magnetic field in the center is simply the magnetic field due to the inner most one. And when I use Ampere's Law, I get the same thing. So basically, I am getting:

B = μ ninner I
 
Physics news on Phys.org
If B is just due to the most inner one, then throw away the other solenoids :biggrin:
Imagine that all the solenoids have nearly the same radius, then if you stand in the center, what you see is one solenoid with current 13I, not I.
 

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Maxwell's Equations: How E and B Fields Interact
Replies
6
Views
2K
What is the Magnetic Field of a Long Solenoid?
Replies
3
Views
2K
I Magnetic field at a point along the solenoid's axis but outside the solenoid
Replies
5
Views
2K
I When is Ampere's Law applicable in different scenarios?
Replies
3
Views
1K
B Calculating Force on an Iron Object with Magnetic Field
Replies
21
Views
4K
Calculating magnetic field outside a solenoid
Replies
15
Views
1K
Engineering Inductance of a layered Solenoid?
Replies
2
Views
998
Understanding self-inductance in a solenoid.
Replies
3
Views
1K
What Force is Needed to Pull a Solenoid in a Magnetic Field?
Replies
3
Views
5K
I How induction works within a coil (nuances of it)
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top