All Questions
8
questions
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
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 ...
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
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 ...
0
votes
0
answers
139
views
Why is the electric field of a naturally equilibrating, isotropic, cylindrical conductor not a function of z (height)?
Some math is presented below to make the question more specific.
TL;DR: If you calculate the electric field of a solid, cylindrical conductor, you find that this field is only a function of radius ...
user213745
0
votes
0
answers
89
views
How to derive the right solution for a linear differential equation of an RC-circuit-like system
In the picture below.
Does anyone knows why all 3 answers are correct and not just answer 2?
Doesn't the answer have to be a negative exponent function?
- 1,053
1
vote
1
answer
1k
views
How to derive resistance as a function of time to keep current constant in circuit?
Having found this answer to an electronics question, a subsequent question would be; in a primitive circuit having only one voltage source or sink in series with a resistor $R$, charging a capacitor, ...
- 26.1k
10
votes
1
answer
367
views
Adding small correction term to ODE solution
Let $\mathbf{r}(t) = [x(t), y(t), z(t)]$ and $\mathbf{v}(t) = \frac{d}{dt}\mathbf{r}(t)$. I'm trying to solve
$$
\frac{d}{dt}\mathbf{v}=\frac{q}{m}(\mathbf{v}\times\mathbf{B}) \tag{1}
$$
where $q$ and ...
- 1,058