All Questions
Tagged with physics electromagnetism
34
questions with no upvoted or accepted answers
4
votes
0
answers
469
views
Deriving boundary conditions at a surface of discontinuity: $\int \mathbf{B} \cdot \mathbf{n} \ dS = 0$
I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.3 Boundary conditions at ...
- 4,322
3
votes
0
answers
130
views
Radial fourier transform of gaussians
In this paper is calculated the square modulus of the radial fourier transform of the function $\rho(r)$
$$\left|F(q)\right|^2=\left| \int_{\mathbb{R}^3} e^{i\mathbf{q}\cdot\mathbf{r}}\rho(\mathbf{r})...
- 275
2
votes
0
answers
60
views
Approximate value of hyperbolic tangent in certain case
I am reading Thé Nature of Magnetism. While reading, I came across a particular approximation of hyperbolic tangent
while in first case $T>T_c$ , it is just Taylor series,
in case $T < T_c$ ( ...
- 21
2
votes
0
answers
54
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Does every field with radial dependence $r^{-2}$ violate Gauss' law for magnetism?
We know that a magnetic field in the form
$$\vec B = k \frac{\hat r}{r^2} \tag{1}$$
where $k$ is a constant, violates Gauss' law
$$\vec \nabla \cdot \vec B = 0 \tag{2}$$
Indeed, we have
$$\vec \...
- 881
2
votes
0
answers
321
views
Galilean transformation law for electric and magnetic fields
Under Galilean transformations between a frame A and another frame B in which A is moving with constant velocity $\mathbf V$, a velocity $\mathbf v_A$ is frame $A$ is seen as $$\mathbf v_B = \mathbf ...
- 21
1
vote
0
answers
65
views
Non-homogeneous wave equation, retarded potentials and causality
Consider the non-homogeneous wave equation in three dimensions with homogeneous initial conditions:
$$
\begin{align}
& \square f(\underline{x}, t) = g(\underline{x},t), \hspace{3mm} \underline{x} \...
- 1,179
1
vote
0
answers
55
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Equilibrium position of $ n $ free charges as polynomials roots
I asked the same question on here but received no answer.
The classic problem of the electrostatic equilibrium positions of a linear system of $ n $ free unit charges between two fixed charges is well ...
- 913
1
vote
0
answers
35
views
Deriving force between continuous distributions of two volume charges without using infinitesimals
We know that force between two point charges is:
$$\vec{F}=k\ q\ q'\ \dfrac{\hat{r}}{r^2}\tag1$$
From here how shall we derive the equation for force between continuous distributions of two volume ...
- 1,141
1
vote
0
answers
73
views
Representing flux tubes as a pair of level surfaces in R^3
I am trying to see if Vector fields(I am thinking of electric and magnetic fields) without sources(divergence less) can be represented by a pair of functions f and g such that the level surfaces of ...
- 341
1
vote
0
answers
579
views
Biot-Savart law on an exponential spiral
A wire carrying a current $I$ is bent into the shape of an exponential spiral, $r = e^θ$, from $\theta = 0$ to $\theta = 2\pi$ as shown in the figure below.
To complete a loop, the ends of the spiral ...
- 21
1
vote
0
answers
91
views
Examples of 2nd Order Differential Equations in Electromagnetism
I am looking for examples of second-order ODE's that are similar to the spring, and pendulum, as well as the LRC, LC, RC, and LR circuits and involve electromagnetism. I know how to solve them, and I ...
- 2,653
1
vote
0
answers
47
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How to compute the magnetic field given a circularly polarised electric field?
The question I have is regarding a solution to a later question (Q2). So in order for the question I have to make sense, unfortunately, I must typeset the previous questions.
(Q1)
We may represent a ...
- 324
1
vote
0
answers
115
views
Vector Calculus - Evaluating $\nabla \times \mathbf{E} = -\frac{1}{c} \partial_t \mathbf{B}$
For the life of me, I cannot remember how to solve equations similar to the cross product equations in Maxwell's equations. I haven't used vector calculus of this level in quite some time and could ...
- 1,021
1
vote
0
answers
301
views
Integral of Coulomb interaction over sphere
I am stuck evaluating an integral that appears in a simplified theory of nuclear binding energy. The nucleus is modelled as a sphere of radius $R$ with a continuous charge distribution, and the ...
- 143
1
vote
0
answers
285
views
area of arbitrary surface element
I am a physics student with a minimal background in differential geometry and I am trying to determine an area element on an arbitrary surface. Suppose we have a surface parameterized by a function $z=...
- 377