All Questions
Tagged with electromagnetism ordinary-differential-equations
20
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Solving 4th order differential equation
I have differential equations such as
$$\frac{1}{\lambda^{2}}\psi_{e}'' = \tanh{\psi_{e}+\psi_{h}}$$
$$\psi_{h}'' - \kappa^{2}\psi_{h} = -\alpha^{2}\tanh{\psi_{e}+\psi_{h}}.$$
Boundary conditions are
$...
- 11
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67
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Solving a funky differential equation.
I'm currently trying to solve the DE that defines charge in a circuit containing an Inductor, Capacitor, Resistor and (crucially) a Memristor. This needs to be able to work for any variable values and ...
- 1
1
vote
1
answer
64
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Absorbing constants when determining them through boundary conditions
I am working through example $3.3$ in Griffiths Electrodynamics in section $3.3$ on Separation of Variables. The example involves solving the $2$-dimensional version of Laplace's Equation for the ...
- 2,220
1
vote
2
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71
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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
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32
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Charge distribution Ohm's law
According to Ohm's law $$\textbf{J}=\sigma\textbf{E}$$
where $\textbf{J}$ is the current, $\sigma$ is the electric conductivity, and $\textbf{E}$ is the electric field. Now from the continuity ...
- 833
1
vote
1
answer
299
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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
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0
answers
91
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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
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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 ...
2
votes
1
answer
78
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Solution of a modified Poisson-Boltzmann equation
I'm trying to solve a modified Poisson-Boltzmann equation given by
$\frac{d^{2}\phi(z)}{dz^{2}}=2k_{1}\sinh(\phi(z))-k_{2}$,
where $k_{1}$ and $k_{2}$ are constants, and I'm not sure of how to solve ...
- 57
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42
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Spatial curves that obey $z'-r^2 \theta' = \text{const.}$ in cylindrical coordinates
I am interested in a class of (arc-length parametrized) curves $\gamma:\mathbb{R} \to \mathbb{R}^3$ with the following property:
If the curve is written in cylindral coordinates $(r,\theta,z)$, it ...
- 179
2
votes
1
answer
166
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Vector differential equation
In electromagnetism we often have a perpendicular constant magnetic field causing a charge to move in a circle. My question is, how do we formally solve this differential equation which involves a ...
- 1,552
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1
answer
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Why do we need both Divergence and Curl to define a vector field?
I was reading Classical Electrodynamics by J.D.Jacskon (section 1.5) where he said:
Perhaps some readers know that a vector field can be specified almost completely if its divergence and curl are ...
- 746
2
votes
0
answers
237
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Modelling Diode current with ODE [closed]
I want to write ODE system for simulating following electrical circuit:
At each small step dt i just do euler integration.
I only know ODE for leaky capacitor:
<...
- 259
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votes
1
answer
76
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can I solve analytically or numerically the equation $\vec{\nabla}\cdot\vec{J}=0$ with the following boundaries?
I was wondering if I can solve somehow the charge conservation equation on a specific domain and boundary conditions.
There is no time dependency, thus the equation reads:
$$\vec{\nabla}\cdot\vec{J}=0$...
- 25
2
votes
2
answers
289
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Setting up and solving this second order nonlinear differential equation
Background
I'm trying to model a system where there are two magnets oriented such that they have attraction forces toward each other. One magnet is in a fixed position and the other magnet, $M$, is ...
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