All Questions
Tagged with calculus electric-fields
42
questions
2
votes
3
answers
301
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 ...
CommunityBot
- 1
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:
$$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
- 97.9k
1
vote
1
answer
40
views
Electric field at a point created by a charged object (derivation/integration process)
I was hoping someone can help me understand the math behind the electric field (electrostatics). I have gaps in my knowledge about integrals and derivatives (university moves very quickly and it has ...
- 207k
4
votes
0
answers
58
views
Energy in electric field of an electron?
I am just trying to get an intuition for the Griffiths equation no. 2.45, where work done to establish a field E is given by
Say we want to solve it for electric field due to an electron (point-charge)...
6
votes
3
answers
590
views
Equation describing the electric field lines of opposite charges
Right now I am preparing for IPhO and the book I had mentions about the "Field lines"
as a curve which has the property which any tangent line to the curve represents the direction of the ...
- 16k
0
votes
1
answer
86
views
What are some ways to derive $\left( \boldsymbol{E}\cdot \boldsymbol{E} \right) \nabla =\frac{1}{2}\nabla \boldsymbol{E}^2$?
For each of the two reference books the constant equations are as follows:
$$
\boldsymbol{E}\times \left( \nabla \times \boldsymbol{E} \right) =-\left( \boldsymbol{E}\cdot \nabla \right) \boldsymbol{E}...
- 54.5k
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
227
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 $P$...
- 12k
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 $$\oint_{\partial S}\vec E\cdot d\vec{A}=\...
- 207k
1
vote
1
answer
113
views
Proof that $\nabla \times E = 0$ using Stoke's theorem [closed]
One way that Jackson proves that $\nabla \times E = 0$ is the following:
$$ 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 ...
- 2,126
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 ...
- 207k
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 ...
- 16k
0
votes
1
answer
359
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?
$$E=k\int \frac{dq}{r^2}.$$
- 207k
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(...
- 207k
3
votes
1
answer
112
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 ...
- 16k
1
vote
2
answers
382
views
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 ...
- 49.9k
0
votes
0
answers
124
views
Line integral across perfect dipole
In problem 4.7 of Griffiths' "Introduction to electrodynamics, 4th Edition", we are asked to find the potential energy of a dipole in an electric field, $\vec{E}$. In the solution, the ...
- 602
0
votes
1
answer
299
views
Equation of infinitesimal ring when finding $ \vec{E}$ of a disc?
When trying to find the electric field created by a uniformly charged disc at a point P on axis of the disc, it can be done by integration.
We start by finding the electric field dE created by each ...
- 1,723
-3
votes
1
answer
101
views
In the statement $\text dV = 4\pi x^2\text dx$ , how is the radius $x^2\text dx$?
I was recently studying a question based on Electrostatics. Here is the link to the question (along with the answer below). I haven't learned integration yet. But my question here is how did we get $x^...
- 349
0
votes
2
answers
195
views
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 $\...
- 12.1k
0
votes
3
answers
141
views
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 (...
CommunityBot
- 1
0
votes
0
answers
38
views
Why is linear approximation of contribution of electric field the same as if whole charge was concentrated at a single point?
I was reading about electric field of uniformly charged ring, of radius $R$, on the axis of the ring at the distance $d$ from the center of the ring and I am confused about usage of differentials. It ...
- 21
1
vote
1
answer
175
views
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 ...
- 2,712
0
votes
0
answers
257
views
Electric field of electric dipole and gradient properties
I am trying to work out whether there is a way to calculate the electric field of a dipole from the following formula:
$$\phi(\vec{r}) = -\vec{p} \cdot\vec{\nabla}\phi_0$$
Where $\phi_0$ is the ...
- 207k
2
votes
3
answers
874
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 ...
CommunityBot
- 1
1
vote
1
answer
137
views
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
0
votes
4
answers
4k
views
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 ...
- 46.1k
-3
votes
3
answers
1k
views
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 ...
- 31
0
votes
1
answer
172
views
The differential of a quantity
I often see the differentials of the electric field strength and the acceleration due to gravity being written as:
$$dE= \mathcal{k}\frac{dQ}{r^2} \tag{1}$$
and
$$dg=\frac{GdM}{r^2} \tag{2}$$
...
- 46.1k
0
votes
1
answer
89
views
Electric field on the boundary of a continuous charge distribution
In Purcell and Morin's Electricity and Magnetism, 3rd Edition, the claim is made that the magnitude of the electric field on the boundary of a continuous charge distribution is finite (assuming the ...
- 207k
1
vote
1
answer
254
views
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 ...
- 6,754
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 ($1.22$):
$$\vec{E}(x,y,z)=\dfrac{1}{4 \pi \epsilon_0}
\int \dfrac{ρ\ (x^\prime, y^\prime, z^\prime)\ \hat{r}\ dx^\...
- 57.2k
0
votes
1
answer
202
views
Divergence of inverse cube law
My intuition tells me that the divergence of the vector field
$$\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{...
- 49.9k
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 $\textbf{D}$ ...
- 49.9k
1
vote
2
answers
4k
views
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?
- 134k
0
votes
1
answer
75
views
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 ...
- 207k
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:
$$
\int_C \mathbf{F} \bullet \, d\mathbf{r}=\int_D\mathbf{F}(\mathbf{r}(t)) \bullet \frac{d \mathbf{r}(t)}{dt} \, dt
$$
...
- 11.3k
0
votes
1
answer
253
views
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 ...
- 125
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 ...
- 207k
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 ...
- 3,148
0
votes
1
answer
1k
views
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 \...
- 6,148