All Questions
129
questions
9
votes
4
answers
668
views
Distribution of point charges on a line of finite length
How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
- 4,194
7
votes
2
answers
784
views
Approximating an expression for a potential
In a problem which I was doing, I came across an expression for the potential $V$ of a system as follows $$V = k\left(\frac{1}{l - x} + \frac{1}{l + x}\right)\tag{1}\label{1}$$ where $k$ is a constant,...
- 1,324
7
votes
5
answers
1k
views
Hollow conductor containing charge: why is internal field cancelled outside and why are the field oustide the cavity zero inside the cavity?
I've a doubt on the following situation. Consider a hollow conductor $A$ (of arbitrary shape) containing another conductor $B$ (again of arbitrary shape), with a positive charge $+q$.
By the ...
- 2,617
6
votes
3
answers
1k
views
Physics olympiad question about a charge capacitor
This is problem 1463 from the Russian magazine Quant.
Unfortunately my Russian is not good enough, so I apologize if the translation of the problem contains errors.
Problem. Inside a flat charge ...
- 417
6
votes
1
answer
6k
views
Calculating the electrostatic energy per unit length of a cylindrical shell surrounded by a coaxial cable
Suppose an infinitely long cylindrical shell of radius $a$ carries a surface charge density $\sigma_0$ and is surrounded by a coaxial cable of inner radius $b$ and outer radius $c$ with uniform charge ...
- 205
4
votes
1
answer
5k
views
Electric field on a spherical shell with a disk cut out
I came across this problem in Electricity and Magnetism by E.M. Purcell:
A spherical shell of radius $a$ is charged with a uniform surface charge density $\sigma$. A small hole of radius $b <<...
- 301
4
votes
3
answers
5k
views
Prove a dielectric with infinite dielectric constant behaves as a conductor for static fields
I read the following problem: Prove that a dielectric medium for which $\varepsilon \to \infty$ behaves as a perfect conductor in the presence of static electric fields.
So, the easy part is that the ...
- 987
4
votes
1
answer
6k
views
Harmonic motion of negative charge between two positive ones [closed]
I have to prove that a negative charge will execute an harmonic motion when placed in the line that separates two positive charges $Q$. (The negative charge $-q$ will not be placed on the center).
I ...
- 501
4
votes
2
answers
4k
views
Electric field in a sphere with a cylindrical hole drilled through it
Suppose that you have a sphere of radius $R$ and uniform charge density $\rho$; a cylindrical hole with radius $a$ ($a\ll R$) is drilled through the center of the sphere, leaving it like a "necklace ...
- 205
3
votes
1
answer
1k
views
Field of a cylinder with surface charge density $\sigma= \sigma_0 \cos(\theta)$
I have this problem, where I have a cylinder with the surface charge density in the title. The angle $\theta$ refers to the angle on the horizontal axis. We had seen a similar exercise with spheres, ...
- 165
3
votes
1
answer
442
views
Theorem for which polarization in a dielectric ellipsoid inside a uniform electric field is constant
I read on textbook that there is a theorem for which, given a dielectric ellipsoid in a external uniform electric field $\bf{E}$, under special conditions on the orientation of $\bf{E}$ with respect ...
- 2,617
3
votes
2
answers
5k
views
The electric field of a conductive sphere containing a charge - grounded vs not grounded
Let's suppose we have a sphere but unlike theoretical ones it'll have some thickness say $\Delta r$ and inner radius $R$. What I was wondering about is how will it behave if we place some charge $q$ ...
3
votes
1
answer
2k
views
Given charge distribution find electric field
Given a charge distribution $\rho(\vec{r})$ where $\vec{r}$ is the position vector and that $\rho$ is a function of only $|x|$, Why is it that the corresponding electric field $E$ is necessarily of ...
- 33
3
votes
2
answers
9k
views
Find the electric field of a uniformly polarized sphere
The problem statement, all variables and given/known data
We want to calculate the field of a uniformly polarized sphere of radius=R
Relevant equations
$$V(\vec{r}) = \frac{1}{4 \pi\epsilon_{0}} \...
3
votes
3
answers
3k
views
Maxwell Stress Tensor in the absence of a magnetic field
I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia,
Start with Lorentz force:
$$\mathbf{F} = ...
- 133