All Questions
Tagged with calculus electric-fields
42
questions
2
votes
3
answers
69
views
$\int \vec{E} \cdot \vec{dA} = (E)(A)$?
I've seen this kind of simplification done very frequently in Gauss's law problems, assuming E is only radial and follows some "simple" geometry:
$$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
- 187
1
vote
1
answer
40
views
Electric field at a point created by a charged object (derivation/integration process)
I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ...
- 19
4
votes
0
answers
58
views
Energy in electric field of an electron?
I am just trying to get an intuition for the Griffiths equation no. 2.45, where work done to establish a field E is given by
Say we want to solve it for electric field due to an electron (point-charge)...
0
votes
1
answer
86
views
What are some ways to derive $\left( \boldsymbol{E}\cdot \boldsymbol{E} \right) \nabla =\frac{1}{2}\nabla \boldsymbol{E}^2$?
For each of the two reference books the constant equations are as follows:
$$
\boldsymbol{E}\times \left( \nabla \times \boldsymbol{E} \right) =-\left( \boldsymbol{E}\cdot \nabla \right) \boldsymbol{E}...
- 105
6
votes
3
answers
590
views
Equation describing the electric field lines of opposite charges
Right now I am preparing for IPhO and the book I had mentions about the "Field lines"
as a curve which has the property which any tangent line to the curve represents the direction of the ...
- 83
1
vote
1
answer
152
views
Unknown integral identity in derivation of first Maxwell equation
Reference: "Theoretische Physik" (2015) by Bartelsmann and others, page 391, equation (11.23).
While deriving the first Maxwell equation based on Coulomb's law, the authors are using the ...
- 183
0
votes
1
answer
220
views
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
1
vote
2
answers
76
views
Question regarding eliminating volume term from Gauss Law
Gauss law is given by
$$\oint_{\partial S}\vec E\cdot d\vec {A}=\dfrac{q_\text{enclosed}}{ε_0}.$$
$$q_\text{enclosed}=\iiint \rho\ dV.$$
For a closed surface $$\oint_{\partial S}\vec E\cdot d\vec{A}=\...
- 367
1
vote
1
answer
113
views
Proof that $\nabla \times E = 0$ using Stoke's theorem [closed]
One way that Jackson proves that $\nabla \times E = 0$ is the following:
$$ 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
0
votes
1
answer
38
views
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 ...
0
votes
0
answers
20
views
Using Variation of Energy for a Dielectric to define the Electric Field
I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
- 1
2
votes
3
answers
235
views
Electric field at a very distant point of an wire from generic point in space
I calculated the electric field at a generic point in the space $P(a,b,c)$ due to an wire with charge density $\lambda$, constant and positive, length $L$, with axis in $z$ direction and origin in the ...
- 23
0
votes
1
answer
358
views
How is this possible (electric field integral)?
In the electric field subject, $dq$ is ok to integral. How is this possible? $Q$ is not even changing variable. Can you explain its math?
$$E=k\int \frac{dq}{r^2}.$$
- 13
1
vote
1
answer
69
views
Calculating the divergence of static electric field without making the dependency argument?
This question is a follow up on this old post here Divergence of electric field
(So this may seem dumb...)
When calculating the divergence of a field point through the following equation, where $\left(...
- 243
3
votes
1
answer
110
views
Nabla commutation in electromagnetism
I don't know how to work with the 'reversed' dot product operator,
$$v\cdot \nabla$$
I arrived to expressions like this trough doing some calculus, and I don't know how to continue with the calculus ...
- 529