All Questions
Tagged with calculus electric-fields
42
questions
1
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2
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382
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Electric field in the center of hemisphere shell without double/triple integrals
I'm trying to derive the electric field in the centre of a solid hemisphere of radius $ R $ where the charge is distributed uniformly. I have seen different methods involving double/triple integrals ...
- 493
1
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1
answer
254
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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 ...
1
vote
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
1
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1
answer
40
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Electric field at a point created by a charged object (derivation/integration process)
I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ...
- 19
1
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1
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113
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Proof that $\nabla \times E = 0$ using Stoke's theorem [closed]
One way that Jackson proves that $\nabla \times E = 0$ is the following:
$$ F = q E $$
$$ W = - \int_A^B F \cdot dl = - q \int_A^B E \cdot dl = q \int_A^B \nabla \phi \cdot dl =
q \int_A^B d \phi = ...
- 284
1
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1
answer
175
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Flux of an inverse square field
This question came in my physics test: What is the value of the surface integral $\oint_S\frac{\overrightarrow{r}}{r^3} \,\cdot\mathrm{d}\overrightarrow{A}$ for r>0?
The professor says that the ...
user208090
1
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1
answer
137
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Other method for finding the equations of the electric field lines
I have an electric potential which, through separation of variables, can be written as $$\phi (x,y)= X(x) \cdot Y(y) =\sum_{n=0}^\infty Cn\cdot \cos(k_n x)\cdot \sinh (k_n y)$$
with $C_n $ and $k_n$ ...
- 548
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1
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86
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What are some ways to derive $\left( \boldsymbol{E}\cdot \boldsymbol{E} \right) \nabla =\frac{1}{2}\nabla \boldsymbol{E}^2$?
For each of the two reference books the constant equations are as follows:
$$
\boldsymbol{E}\times \left( \nabla \times \boldsymbol{E} \right) =-\left( \boldsymbol{E}\cdot \nabla \right) \boldsymbol{E}...
- 105
0
votes
3
answers
141
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Problem in finding the divergence at a point [duplicate]
I am solving a problem given as
Divergence of $\frac{\textbf{r}}{r^3}$ is
a) zero at the origin
b) zero everywhere
c) zero everywhere except the origin
d) nonzero everywhere
The answer is given as (...
- 436
0
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4
answers
4k
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I don't understand the logic/concept of $\mathrm dQ=\lambda\,\mathrm dx$. How did we arrive at this expression?
So I've been learning Electrostatics. So while solving for the Electric Field Due to an infinite positively charged rod, I encountered the following expression on the internet wherein the following ...
0
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2
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195
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Does the number of field lines crossing an area depend upon angle between them?
Consider Electric Field Lines crossing a square area (for simplicity) such that all field lines are parallel and make an angle say $\alpha$ with the area vector of the square.
Let us vary the angle $\...
- 1,568
0
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1
answer
202
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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
$$ \vec{\nabla}\cdot \vec{...
- 453
0
votes
1
answer
1k
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Gauss's (Divergence) theorem in Classical Electrodynamics
How does divergence theorem holds good for electric field.
How does this hold true-
$$\iiint\limits_{\mathcal{V}} (\vec{\nabla}\cdot\vec{E})\ \mbox{d}V=\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \...
- 772
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1
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227
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How should I interpret these integrals from Griffiths 'Intro to Electrodynamics'?
The book defines the electric field at a point $P$ a distance $r$ due to a point charge $q$ as:
$$ E = \frac{1}{4\pi \epsilon _0} \frac{q}{r^2}$$
it then tells us that the electric field at a point $P$...
- 345
0
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1
answer
38
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Spherical and Cartesian forms of divergence [closed]
Suppose the electric field found in some region is $$\overrightarrow{E} = ar^3\vec{e}_r$$ in coordinates
spherical (a is a constant). What is the charge density?
So, using the spherical form of ...
