All Questions
19
questions
1
vote
1
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98
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Electrostatic potential outside of a charged ball [closed]
To preface, I have never solved Maxwell's equation or his resulting Poisson's equation in any coordinate scheme, nor am I a physics major. I'm entirely teaching myself how to do this, so I don't know ...
- 121
2
votes
1
answer
63
views
Does the geometric shape of the cross-section of an infinitesimally thin conducting charged thread (wire) affect its electric field?
Assume that a solid conducting torus (toroidal ring), with a cross-section of a circle of (minor) radius $r$, is negatively charged. Solving Poisson's equation, we can find the charge distribution of ...
- 2,503
1
vote
2
answers
159
views
Does cutting out the surfaces with no surface charge affect the charge distribution on the remaining parts of a conducting surface of arbitrary shape?
Assume that we have an arbitrary conducting surface being charged positively/negatively. Also, assume that we have extracted charge distribution by solving the Poisson's equation with proper boundary ...
- 2,503
4
votes
1
answer
165
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Series Solution of Laplace Equation in Spherical Coordinates
I was recently Studying Griffiths Electrodynamics after a long time and there I saw the Laplace equation. Because it was my second time going over Griffiths so I thought maybe I should try to derive ...
- 585
0
votes
1
answer
68
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Equation of a equipotential surface
I have been trying to find a equation for the equipotential surface of a dipole , so I started with a simpler system of a singular charged particle , here are few things I know about the equipotential ...
- 5
2
votes
1
answer
85
views
Solution to Laplace equation in spherical coordinates and Legendre polyomials
I have the following problem:
A metallic sphere of radius $R$ is placed in a region where there is an electric field $\vec{E} = E_0 \vec{e_z}$. Solve Laplace equation for the scalar potential $V(r, \...
- 89
0
votes
1
answer
183
views
How many boundary conditions do we need to solve Laplace's equation?
I'm struggling to understand which boundary conditions are necessary to solve Laplace's equation. In order to better understand them, I have thought of a scenario that I would like to ask a couple of ...
- 941
1
vote
1
answer
118
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Legendre series solutions for the Laplace equation: can Neumann boundary conditions be applied?
In Jackson E&M, it is shown in equation (3.33) that the Laplace equation with azimuthal symmetry can be expanded in Legendre series in spherical coordinates,
$$ \Phi(r,\theta)=\sum_{l=0}^\infty\ [...
- 31
0
votes
1
answer
176
views
Cylindrical capacitor and charge density per unit area [closed]
I am dealing with the following problem:
Assume that a charge has been placed on the inner cylinder, and that the entire charge is distributed on the outer surface of the inner cylinder as shown in ...
- 39
2
votes
2
answers
1k
views
Faraday's law: How to interpret flux on a time/voltage graph?
Background
This is related to a homework assignment, but my question is more on the conceptual side. I will therefore only paraphrase the problem.
Problem
The question begins with the idea of dropping ...
- 163
1
vote
1
answer
347
views
Boundary condition for Green's function [closed]
Suppose we have an equation $\nabla^2V = -\rho/\epsilon_0$ and the boundary condition for $V$ is given. I have a question regarding the boundary condition for Green's function for this equation. What ...
- 31
0
votes
2
answers
134
views
Why electric potential is separable?
In Electrostatics, if we consider a region without charges the electrostatic potential $V$ obeys Laplace's Equation $\nabla^2 V = 0$. We can tackle this with separation of variables. In cartesian ...
- 5
0
votes
1
answer
189
views
What can the solution to Laplace's equation tell us?
If $V$ satisfies ${\nabla}^2V=0$ given the boundary conditions associated to the boundaries of some volume $\tau$ in space, then what can $V$ tell us?
Does it tell us the potential in all of space? Or ...
- 692
1
vote
2
answers
549
views
How to determine charge density using Dirac deltas in advance? --- not after the fact
Context
I have already asked one question regarding charge densities, Diracs, and Heavisides [0]. At the time of writing, that question remains open. More importantly, I still remain unclear regarding ...
- 460
0
votes
1
answer
57
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What is the electric field inside this shell? [duplicate]
A problem from Griffiths asks us to find the electric potential inside and outside a spherical shell. The potential on the shell is specified to be $V(R, \theta) = k \cos(3\theta)$. There is no charge ...
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