Electric field inside a dielectric sphere with cavity

AI Thread Summary
The discussion centers on calculating the electric field inside a dielectric sphere with a spherical cavity, specifically addressing the implications of different permittivities for the materials involved. The original problem involves a nonconducting sphere with a uniform charge density and a cavity, raising questions about whether to use the dielectric constant of the sphere or the vacuum permittivity for the cavity. Clarifications are made regarding the treatment of an imaginary sphere with negative charge density and its material consistency with the surrounding sphere. Comparisons are drawn to a separate problem involving a toroid with different permeability materials, highlighting the differences in approach due to charge distribution. The conversation concludes with an acknowledgment of the complexities involved in these calculations.
Leotron
Messages
3
Reaction score
0
Original Problem:

"A sphere of radius a is made of a nonconducting material that has a uniform volume charge density [PLAIN]http://jkwiens.com/2007/10/24/answer-electric-field-of-a-nonconducting-sphere-with-a-spherical-cavity/d2606be4e0cd2c9a6179c8f2e3547a85_2.gif. A spherical cavity of radius b is removed from sphere which is a distance z from the center of the sphere. Assume that a > z + b. What is the electric field in the cavity?"

I understand how to solve an ordinary problem like this, but what if the sphere has dielectric constant ε which is different from the cavity whose permittivity is ε0? When solving this, should I treat the imaginary small sphere with -ρ to have permittivity ε or ε0?
 
Last edited by a moderator:
Physics news on Phys.org
The imaginary sphere has the same material as the sphere around it. Not sure if that influences the result at all.
 
  • Like
Likes Jilang
mfb said:
The imaginary sphere has the same material as the sphere around it. Not sure if that influences the result at all.
But when I was doing another problem which deals with calculating the self inductance of a toroid with a small gap, whose permeability is μ for the iron part and μ0 for the gap, the answer uses μ0 to calculate the B field in the gap (used "imaginary wire loop")...And the answer is definitely different using ε/ε0 in the sphere case. Still not sure why. Maybe the answer of that problem is wrong...
 
For the toroid magnet, you don't remove something, you treat it as circle with two different materials the whole time. And you don't have a charge distribution as you have here.
 
mfb said:
For the toroid magnet, you don't remove something, you treat it as circle with two different materials the whole time. And you don't have a charge distribution as you have here.
Woo that makes sense...Thanks!
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top