All Questions
Tagged with calculus electric-fields
42
questions
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
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)...
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
2
votes
4
answers
5k
views
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
votes
3
answers
871
views
Line integral of a point charge
I am trying to teach myself Electrodynamics through self-study of Griffiths' Introduction to Electrodynamics, and I am having difficulty with a calculation that involves a line integral of a point ...
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:
$$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
- 187
2
votes
3
answers
235
views
Electric field at a very distant point of an wire from generic point in space
I calculated the electric field at a generic point in the space $P(a,b,c)$ due to an wire with charge density $\lambda$, constant and positive, length $L$, with axis in $z$ direction and origin in the ...
- 23
2
votes
1
answer
949
views
Electric field at any point due to a continuous charge distribution
I am reading Purcell and Morin's Electricity and Magnetism 3rd Edition.
Equation ($1.22$):
$$\vec{E}(x,y,z)=\dfrac{1}{4 \pi \epsilon_0}
\int \dfrac{ρ\ (x^\prime, y^\prime, z^\prime)\ \hat{r}\ dx^\...
- 91
2
votes
1
answer
1k
views
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 $\textbf{D}$ ...
2
votes
1
answer
3k
views
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
2
votes
3
answers
298
views
Mathematical Ambiguity in Electric field at centre of a uniformly charged hollow hemisphere
So, there is a question in the book "Problems in General Physics" by I.E. Irodov to calculate the electric field at the centre of a hollow hemisphere.
I was able to solve this question and ...
- 35
2
votes
0
answers
366
views
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
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
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
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