All Questions
Tagged with calculus electric-fields
42
questions
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1
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Why did we take gradient outside the integral sign in Scalar potential derivation?
I tried to understand the reasoning given in it but I couldn't understand it. It says that "as the gradient operation involves x and not the integration variable x', it can be taken outside the ...
2
votes
1
answer
949
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Electric field at any point due to a continuous charge distribution
I am reading Purcell and Morin's Electricity and Magnetism 3rd Edition.
Equation ($1.22$):
$$\vec{E}(x,y,z)=\dfrac{1}{4 \pi \epsilon_0}
\int \dfrac{ρ\ (x^\prime, y^\prime, z^\prime)\ \hat{r}\ dx^\...
- 91
0
votes
1
answer
199
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Divergence of inverse cube law
My intuition tells me that the divergence of the vector field
$$\vec{E} = \dfrac{\hat{r}}{r^3} $$
should be zero everywhere except at the origin. So I think it should be
$$ \vec{\nabla}\cdot \vec{...
- 453
2
votes
1
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1k
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Curl of P in a symmetric problem
I was reading Introduction to Electrodynamics by Griffiths, and I'm stuck on 4.3.2. He says:
If the problem exhibits spherical, cylindrical or plane symmetry, then you can get $\textbf{D}$ ...
1
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2
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4k
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How is the curl of the electric field of a dipole zero?
For a static charge, the curl of the electric field is zero. But in the case of a static dipole the electric lines of force curl. How it that possible?
- 21
-3
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3
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1k
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Why is the electric potential on the surface of a sphere not infinite?
By using Gauss' Law, it can be shown that a uniformly charged hollow sphere can be treated as a point charge lying at its centre with a charge equal to that of the sphere. Owing to this fact, the ...
- 135
0
votes
1
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75
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Practice Superposing Fields Integral
I've been doing practice problems from Andrew Zangwill's Modern Electrodynamics as I have an exam next week. I am having a bit of difficulty following this integral in the solution's manual:
How do ...
- 13
2
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1
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3k
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How to set up line integral of electric field? Confused over notation
In multivariable calculus the line integrals was parameterized and denoted:
$$
\int_C \mathbf{F} \bullet \, d\mathbf{r}=\int_D\mathbf{F}(\mathbf{r}(t)) \bullet \frac{d \mathbf{r}(t)}{dt} \, dt
$$
...
- 433
0
votes
1
answer
253
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Electric field uniform circle $R$ direction cancel out
I am doing a physics problem involving a uniform circle with a total charge of X, and am attempting to find the electric field on a point charge on the axis of the circle a distance of Z away.
I ...
- 411
2
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4
answers
5k
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Electric Field due to a disk of charge. (Problem in derivation)
This might be a really silly question, but I don't understand it.
In finding the electric field due to a thin disk of charge, we use the known result of the field due to a ring of charge and then ...
- 278
2
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0
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366
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insulator based gauss law questions
My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.
Here's a question I'm working on that isn't part of my book.
where the radii ...
- 225
0
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1
answer
1k
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Gauss's (Divergence) theorem in Classical Electrodynamics
How does divergence theorem holds good for electric field.
How does this hold true-
$$\iiint\limits_{\mathcal{V}} (\vec{\nabla}\cdot\vec{E})\ \mbox{d}V=\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \...
- 772