All Questions
Tagged with homework-and-exerciseselectrostatics
1,333 questions
-1votes
0answers
20views
Infinite Hexagon Grid of Resistors [closed]
How to find the equivalent resistance between two opposite points, the resistor between any two points is R. For adjacent and one point apart, the answer comes out to be R but cannot do the same for ...
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2votes
0answers
78views
$3$ Identical point charges placed on the vertices of an equilateral triangle [closed]
So I was solving a book on electrostatics and I stumbled upon this question that I could not solve in any sort of an elegant or simple way. The question is as follows,"$3$ identical point charges ...
2votes
1answer
56views
When a cylindrical conductor is kept between $2$ charges of opposite signs, how does the net force acting on each charge change?
This was a question that appeared in my recent electrodynamics test. A thin cylindrical rod $\mathrm{AB}$ is introduced between $2$ charges $+\mathrm q_1$ and $-\mathrm q_2$. Qualitatively examine ...
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0votes
0answers
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Poisson's Equation outside of a sphere given a finite distribution of point sources. I am mostly concerned with the definition of Green's function
$$\nabla^2 V = F(\textbf{r}) \\ F(\textbf{r}) = \cases{0 & $0\le r \le a$ \\ \frac{1}{r^2}\sin\theta\cos\theta\sin\phi & $a<r<2r$ \\ 0 & $2a\le r<\infty$}\\ V(a,\theta,\phi) = 0 $$...
- 173
0votes
1answer
41views
The movement of an electric charge within an electric field and a magnetic field [closed]
What is the force acting on a charged particle with charge q moving in the presence of an electric field E and a magnetic field B with an initial velocity V? Assuming that the fields are perpendicular,...
1vote
2answers
73views
I can't get the Cartesian Multipole expansion correctly with index notation. Is there a better way?
What I did: $$ \frac{1}{|\vec{x} - \vec{x}'|} = \frac{1}{r} - x'_i \nabla_i \frac{1}{r} + \frac{1}{2} x'_i x'_j \nabla_i \nabla_j \frac{1}{r} + \dots $$ $$ = \frac{1}{r} - x'_i \frac{x_i}{r^3} + \frac{...
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0votes
1answer
84views
Electric field intensity due to a point charge inside a hollow conductor [closed]
Suppose I have a hollow spherical conductor and a charge Q placed off-center inside the conductor (at a distance R from the center). What would be the electric field intensity at say the center of the ...
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0votes
1answer
72views
Homework Question related to electric field and gauss law [closed]
My doubt lies in the first (a) option. I can find the electric field due to that small hole (individually) using $E=q/(4\pi \varepsilon_0 r^2)$ and i get my answer. But when I tried using gauss law ...
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0votes
0answers
23views
Sign issue with the boundary integral of Green's Function
I feel it crucial to start by writing out the derivation of the solution to Poisson's equation using Green's formula: $$\nabla \cdot \phi \nabla \psi = \phi\nabla^2\psi + \nabla\phi\cdot\nabla\psi$$ ...
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0votes
1answer
25views
Do we have to consider the horizontal vector distance when calculating potential difference in a uniform electric field in positive $x$ direction? [closed]
I was solving a question from a previous year question paper of the CBSE board exam that read: A uniform electric field E of 500 N/C is directed along +X axis. O,B and A are three points in the field ...
0votes
0answers
44views
How to derive 3D Green's function for a source outside of a grounded conducting sphere using method of images?
In Jackson's $\textit{Classical Electrodynamics}$, We have at the start of section 2.6, equation (2.16) $$G(\textbf{x},\textbf{x}') = \frac{1}{|\textbf{x}-\textbf{x}'|} - \frac{a}{x'|\textbf{x}-\frac{...
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1vote
0answers
90views
Multi-plate capacitor US physics olympiad 2008 problem A1 [closed]
In the solutions I used a different approach by assuming $\sigma_1, -\sigma_2, \sigma_2, -\sigma_1$(because of symmetry and field outside has to be zero) as in problem 3.21 from E and M Purcell. I ...
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0votes
1answer
53views
Slight discrepencies between solution to Poisson's equation from convoluting Green's function vs separation of variables using spherical harmonics
Given a grounded conducting sphere of radius $a=1$, we want the electrostatic potential which solves: $$\Delta V(r,\theta,\phi) = -\rho \\ \rho = \cases{1 & $0<r<a$ \\ 0} \\ V(a,\theta,\phi) ...
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0votes
0answers
44views
Voltage across Capacitor in Series after shorting internal capacitor
I have what appears to be a very simple question, but I have not seen it asked anywhere and would like to verify my solution is correct. Imagine that you have 3 capacitors in series, each with an ...
- 133
3votes
1answer
59views
Debugging a Kelvin Water Dropper [closed]
For a high school project, I have to build a Leyden jar, ideally functional... So to charge it, I'm trying to build a Kelvin Water Dropper. After 2 weeks of trying, and it being due on Monday, I can ...
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