All Questions
Tagged with physics electromagnetism
101
questions
2
votes
3
answers
83
views
How to compute the volume integral for the potential of an arbitrary point outside a uniformly charged ball?
$$\frac{\rho}{4\pi\epsilon_0}\iiint_{D}^{}\frac{1}{\left\| \mathbf{r}-\mathbf{r'} \right \| }dV'$$
$D$ is a ball of radius $R$
$\mathbf{r}$ is the position vector of the point where we want to ...
- 163
0
votes
1
answer
75
views
What integral is used to calculate the electric field generated by a continuous charged curve?
I'm studying Multivariable Mathematics, by Ted Shifrin, in which one reads that ''the gravitational force exerted by a continuous mass distribution $\Omega$ with density function $\delta$ is
$$\mathbf{...
0
votes
0
answers
34
views
Boundary Conditions on the Magnetic Flux Density (B-field)
My question is similar to this one (Boundary conditions magnetic field) in that it is related to the boundary conditions of the magnetic field (B-field). However, my question focuses on mathematically ...
- 665
1
vote
2
answers
77
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What does $\vec{\nabla}^2 \vec{E} = \vec{\nabla}^2 \left[ f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0 \right]$ mean?
$\vec{E} = f(\vec{k} \cdot \vec{r} - \omega t) \vec{E}_0$ with the constant vector field $\vec{E}_0$
I only know the case if I apply the Laplacian operator on a scalar field, in this case it is a ...
14
votes
3
answers
3k
views
What is the sum of an infinite resistor ladder with geometric progression?
I am trying to solve for the equivalent resistance $R_{\infty}$ of an infinite resistor ladder network with geometric progression as in the image below, with the size of the resistors in each section ...
- 1,111
0
votes
0
answers
66
views
Calculate Electric Field on the Z-axis from a finite charge wire
I've been trying to find the electric Field on the Z-axis from a non-uniform charge density line charge. The wire is placed on the z-axis from $z=0$ to $z=1$, $E=?$ at $z>1$ and $z<0$
$$
\rho =...
- 1
0
votes
0
answers
63
views
Vector Line Integral For Biot Savart Law
How would one go about computing the vector line integral presented in the Biot-Savart law: $$\vec{B}=\int_c\frac{\mu_0I}{4\pi} \frac{d\vec{l}\times\hat{r}}{r^2}$$
I know how to compute vector line ...
- 33
0
votes
0
answers
63
views
Electric field flux proportional to the field lines generated by (for example) a static charge
Suppose we have a stationary positive charge at a point in space that we call $+Q$. We know by definition that the flow of the electrostatic field is given by, in its simplified form,
$$\Phi_S(\vec E)=...
- 7,792
1
vote
1
answer
93
views
Distance becoming equal to displacement
Consider a charged particle of charge q and mass m being projected from the origin with a velocity u in a region of uniform magnetic field $\mathbf{B} = - B \hat{\mathbf{k}} $ with a resistive force ...
- 333
8
votes
1
answer
711
views
A calculus problem from electrostatics
Since this problem consists of multiple parts and one needs to see all of them to understand the problem i'm going to list out all of them:
Consider a uniformly charged spherical shell of radius $R$ ...
- 429
1
vote
0
answers
65
views
Non-homogeneous wave equation, retarded potentials and causality
Consider the non-homogeneous wave equation in three dimensions with homogeneous initial conditions:
$$
\begin{align}
& \square f(\underline{x}, t) = g(\underline{x},t), \hspace{3mm} \underline{x} \...
- 1,179
4
votes
1
answer
70
views
Linear system $Ax=y$ with partially known $x,y$ and non singular $A$
PHYSICAL INTUITION
While proving the equivalence between the Dirichlet problem (i.e. the potential is known on the surface of every conductor) and the mixed problem (i.e. the potential is known on ...
- 1,179
6
votes
1
answer
162
views
Effective resistance in finite grid of resistors
Consider a $m\times n$ grid of one-Ohm resistors. What is the effective resistance of any given edge? I understand how to do the case $m=2$ inductively using the series and parallel laws, but I get ...
- 1,147
1
vote
0
answers
55
views
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
0
votes
2
answers
155
views
Taylor Expansion for a configuration of $2$ point charges on a line
Was getting back into physics and reading a chapter on electrostatics which sets up the following situation. We have a configuration of point charges - one $-q$ at the point ($-d,0,0$) and one $+q$ at ...
- 2,220
2
votes
2
answers
1k
views
Finding the distance from a point a distance $z$ above the center of a square to any point on the edge
I was working on an electrostatics problem that I thought I was doing correctly. However, upon reading the solution I see I was not. I will post my attempt and the solution below and then ask a few (...
- 2,220
1
vote
1
answer
59
views
"Double" relativistic variant of the same classical mechanics equation
This question is about my curiosity about the relativistic Kepler equation of which I am reading in a recent paper. Actually, I am only interested in an introductory concept stated in paper.
Let
$$ m\...
- 3,277
0
votes
1
answer
119
views
Help with a physics problem about the magnetic field
Text of the problem:
A circular loop of radius $R$ carries a current $I_1$. Perpendicular to the plane of the coil, and tangent to it, there is an indefinite rectilinear wire, traversed by a current $...
0
votes
0
answers
82
views
Electric Field felt at the origin of a hemisphere
I want to calculate the Electric Field that is felt at the origin $O$ provoked by a hemisphere of radius $R$ with uniform charge density $\sigma$.
I used spherical coordinates: $\vec{r} = -R(\sin(\phi)...
- 653
0
votes
0
answers
34
views
Translational invariance of sources/materials implies translational field invariance
Let's say we have an electromagnetic problem where $\epsilon = \epsilon(x,y)$, $\rho = \rho(x,y)$, and $J = J(x,y)$. The physicist argument is that by the symmetry of the problem we also have $E = E(x,...
- 613
4
votes
1
answer
158
views
Properties about an elliptic integral of the first kind.
In polar coordinates, the electric potential of a ring is represented by the next relation
$$
\frac{\lambda}{4\pi\varepsilon_0}\frac{2R}{|r-R|}\left( F\left(\pi -\frac{\theta}{2}\Big|-\frac{4 r R}{(r-...
- 51
1
vote
2
answers
71
views
Boundary Problem for Electrostatic Potential
I have been working on a exercise that asks me to resolve the 2nd order differential equation for a electrostatiic problem. Here it is the exercise statement:
Letting u be the electrostatic potential ...
- 13
4
votes
2
answers
145
views
Flux integral of Gauss law
Consider a point charge enclosed by some surface, using spherical coordinates, and taking $\hat a$ to be the unit vector in the direction of the surface element, flux is
$$\oint\vec E\cdot d\vec A = ...
3
votes
2
answers
318
views
Is curl of a particle's velocity zero?
The question
Consider the motion of a particle specified by $\mathbf{x} (t): \mathbb{R} \mapsto \mathbb{R}^3$, where $\mathbf{x} = (x_1,x_2,x_3)$ in cartesian coordinates. The curl of its velocity $\...
- 33
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
0
votes
1
answer
249
views
Using "Maxwell's curl equations" to get $H_y = \dfrac{j}{\omega \mu} \dfrac{\partial{E_x}}{\partial{z}} = \dfrac{1}{\eta}(E^+ e^{-jkz} - E^- e^{jkz})$
I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Chapter 1.4 THE WAVE EQUATION AND BASIC PLANE WAVE SOLUTIONS says the following:
The Helmholtz Equation
In ...
- 4,322
2
votes
1
answer
126
views
What does it mean to say that "$h$ is a coordinate measured normal from the surface"? How does this work in practice?
I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Section Fields at a General Material Interface of chapter 1.3 FIELDS IN MEDIA AND BOUNDARY CONDITIONS says ...
- 4,322
2
votes
1
answer
187
views
Calculating the average of the square of the magnitude of an electric field
Let the sinusoidal electric field polarised in the $\hat{x}$ direction be $\overline{\mathcal{E}}(x, y, z, t) = \hat{x}A(x, y, z)\cos(\omega t + \phi)$, where $A$ is the amplitude, $\omega$ is the ...
- 4,322
1
vote
1
answer
101
views
Can we have vectors with vectors as components?
I was working on my course on Electrodynamics earlier today, when I was tasked with computing the eletric field of a non-trivial charge distribution, and it struck me that I had a field with ...
- 487
1
vote
1
answer
437
views
How does $\sqrt{-\omega^2(\epsilon - j\sigma/\omega)\mu}$ having either a positive or negative sign determine $\alpha_0$ and $\beta_0$?
I am told that Maxwell's equations take the form
$$\text{curl} \ \mathbf{E} = - \mu j \omega \mathbf{H}, \ \ \ \ \ \text{curl} \ \mathbf{H} = (\sigma + \epsilon j \omega) \mathbf{E},$$
where $\sigma$ ...
- 4,322
2
votes
2
answers
77
views
$i = \frac{dq}{dt}$ implies $\Delta q = i \Delta t$? Incorrect mathematics used as some kind of hand-wavy justification for an engineering equation?
I am reading an electrical engineering textbook that states that the relationship between current $i$, charge $q$, and time $t$ is
$$i = \dfrac{dq}{dt} \tag{1}$$
Based on this, the authors then state ...
- 4,322
1
vote
0
answers
35
views
Deriving force between continuous distributions of two volume charges without using infinitesimals
We know that force between two point charges is:
$$\vec{F}=k\ q\ q'\ \dfrac{\hat{r}}{r^2}\tag1$$
From here how shall we derive the equation for force between continuous distributions of two volume ...
- 1,141
2
votes
1
answer
76
views
Variational derivation of *all* covariant Maxwell's equations?
If I suppose there exists a 4-"vector potential" $A\in\Omega^1(U)$ such that the Faraday 2-form satisfies $F = dA$ (which is equivalent to assuming the homogeneous Maxwell's equations $dF=0$ ...
- 7,532
0
votes
0
answers
76
views
Electric field with $\nabla \times \vec{E} = 0$ and $\nabla \cdot \vec{E} = 0$ outside of a conductor circulates a constant electric current
Q: suppose that I know that outside of some conductor circulates a constant electric current , I have $\nabla \times \vec{E} = 0$ and $\nabla \cdot \vec{E} = 0$. How do I prove that $\vec{E} = 0 $ ...
- 95
1
vote
0
answers
73
views
Representing flux tubes as a pair of level surfaces in R^3
I am trying to see if Vector fields(I am thinking of electric and magnetic fields) without sources(divergence less) can be represented by a pair of functions f and g such that the level surfaces of ...
- 341
4
votes
2
answers
118
views
Can a small change to the magnetic field result in infinite changes to the vector potential?
Consider a magnetic field, $\mathbf{B}(x,z)$ given by
$$\begin{aligned}
\mathbf{B}(x,z) &= [B_x(x,z),\ B_y(x,z),\ B_z(x,z)] \\
&= \left[-\frac{l}{k}\cos(kx),\ -\sqrt{1-\frac{l^2}{k^2}}\cos(kx),...
- 1,027
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
1
answer
299
views
Origin of Legendre's constant term.
I'm that student who needs to know where does something comes from. I have been studying Differential Equations and Electrodynamics (I'm a physics student), and I was wondering why we (in physics) use ...
0
votes
1
answer
123
views
Electric Field and Direction of Field
I want to measure the magnitude, and the direction of the electric field at point P induced by a rod that has a charge of $-22.0\mathrm{\mu C}$. The problem has been accurately dimensioned. The ...
- 2,653
-1
votes
1
answer
74
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Physics Problem with Coulomb's Law and One Axis
I have 3 point charges placed at the x-axis in the table below I will show their positions.
\begin{array}{|c|c|c|c|}\hline\mathrm{q_1}&2\ \mathrm{\mu C}&x_1&0\ \mathrm{m}\\ \hline \mathrm{...
- 2,653
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
0
votes
0
answers
65
views
Why is the integral of this term zero?
I came upon a problem in my physics textbook and had a question as to why term was equal to zero.
The equation and its integration :
\begin{align}
B &= u(H+I)
\\
dB&= u dH + udI
\\
\int HdB &...
1
vote
1
answer
190
views
Electric field of a charge uniformly distributed on a plane
I am supposed to calculate the electric field $E$ created by a electrical charge $Q>0$ distributed on the surface of a plane. For this I should use
(i) Gauss' theorem $$\int_M \operatorname{div}(...
- 2,085
1
vote
0
answers
91
views
Examples of 2nd Order Differential Equations in Electromagnetism
I am looking for examples of second-order ODE's that are similar to the spring, and pendulum, as well as the LRC, LC, RC, and LR circuits and involve electromagnetism. I know how to solve them, and I ...
- 2,653
0
votes
1
answer
323
views
end-to-end resistance of a truncated cone
Basically the question is the resistance of the whole truncated cone which has top and bottom coal-flaps with radius $r_1$ and $r_2$. I have the $r(x)$ given by a function. I know that I have to ...
- 103
0
votes
0
answers
24
views
Beam propagation in an optical fiber with a $\tanh(\cdot)$ refractive index profile
The differential equation for a optical fiber with a refractive index $n(r)$ is given as
$$\nabla^{2}_{\perp}A(r,\theta)+(k^{2}n(r)^2-\beta^2)A(r,\theta)=0.$$
which is separable in cylindrical ...
1
vote
0
answers
47
views
How to compute the magnetic field given a circularly polarised electric field?
The question I have is regarding a solution to a later question (Q2). So in order for the question I have to make sense, unfortunately, I must typeset the previous questions.
(Q1)
We may represent a ...
- 324
3
votes
2
answers
392
views
'Ugly' Simultaneous equations with 4 variables
I have to solve the following 'Ugly' Simultaneous equations to solve a problem on my textbook of physics. The problem is originally discussed on the thread but, it was unfortunately categorized by ...
- 665
0
votes
0
answers
221
views
Deriving the wave equation
Given:
$$\nabla \times \mathbf H = \frac{4\pi}{c} \mathbf j \ \ \ \ \ \ \ \ \ (1)$$
$$\nabla \times \mathbf E = -\frac{1}{c} \frac{\partial \mathbf H}{\partial t} \ \ \ (2)$$
$$\...
- 1,139
0
votes
2
answers
71
views
Integral of electric field $E$ is $0$ implies that the field is $0$?
If we consider $\vec{E}$ the electric field in $R^n$ and we have :
$$\int_{R}^{\infty}\vec{E}(\vec{r})d\vec{r}=0$$
where $R$ is in $R^n$ and $\vec{r}$ is in $R^n$
$$\vec{E}(\vec{r})=\frac{1}{4\pi \...
- 526