Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [electromagnetism]

For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.

For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include (algebra-precalculus), (vector-analysis), and (fourier-analysis).

396 questions
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How can I expand on this part of this proof concerning magnetic fields?

I am supposed to prove: $$B_y=\frac{\mu_0}{4\pi}Iaz\int_{0}^{2\pi} \frac{\sin\phi}{(a^2+y^2+z^2-2ay\sin\phi)^{3/2}}d\phi=\frac{\mu_0Ia^2}{4r^3}\biggl(\frac{3yz}{r^2}\biggl)$$ and $$B_z=\frac{\mu_0}{4\pi}Iaz\int_{0}^{2\pi} …
David1607
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Jackson's Electrodynamics, exercise 5.34, using Laplace solutions to prove a relation about mutual inductance

I've managed to solve 5.34 (a) and (b) of Jackson's electrodynamics. Right this minute I believe I know how to solve (c) but I am not certain yet and need some help on this. It is not a trivial problem. The geometry is as such, Two identical…
Kevin Njokom
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Finding an electrostatic potential, from green function and charge density, setting up and calculating

I have been given a charge density in 2 dimensions. $\sigma (\rho, \phi) = \frac{\lambda}{a} \sum_{n = 0}^3 (-1)^n \delta(\rho - a) \delta( \phi - \frac{n \pi}{2}) $ I have also been reminded about a Green function from a previous…
Kevin Njokom
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showing explicitly by separation of variables in polar coordinates that the green function can be expressed as Fourier series in azimuthal coordinate

I am working on a problem in Jackson that asks me to show explicitly by separation of variables in polar coordinates that the green function can be expressed as Fourier series in azimuthal coordinate, $G = \frac{1}{2 \pi} \sum_{-{\infty}}^{\infty}…
Kevin Njokom
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dipole in a dielectric sphere

I rather stuck on this homework question. I have been working on it for 3 days. I need a little help. Context A point dipole p is placed at the centre of a dielectric sphere with permittivity $\varepsilon$ and radius $R$. A set of axes are chosen…
podge cassidy
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How to find the magnetic field between two connected current-carrying wires?

How do I find the magnetic field at point $b$, very far from $a$? I know the magnetic field due to 1 current-carrying wire is $$B = \frac{\mu_0 i}{2\pi R}$$ So, does that mean the magnetic field at point $b$ is $$B = B_{top\,wire} + B_{bottom\,…
NestorV S
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Gauss Law and Potentials

The infinite plane $z = 0$ is earthed and the infinite plane $z=d$ carries a charge of $\sigma$ per unit area. Find the electrostatic potential between the planes. I have tried to compute the electric field between the two plates;the field…
MathematicianP
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Magnetostatics Vector potential infinite straight wire

I have found the vector potential for a circuit $C$ carrying current $I$ such that $C$ is a segment of the z-axis $-L$ and $L$ to be $A(r)=\frac{\mu_0k}{4\pi}I\ln\frac{L+\sqrt{\rho^2+L^2}}{-L+\sqrt{\rho^2+L^2}}$ where $\rho$ is the distance from an…
dahaka5
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Maxwell Equations and Flux Continuity Law

Use Maxwell’s second equation (Faraday’s law) to prove the flux continuity law: ${\rm div} (B) = 0$, where $B$ is time-varying. My approach would be to prove the flux continuity law using Gauss' Law for magnetic fields, but I'm unsure on how to…
Adam
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Electrostatics electric charge on an infinite plane

I have the following question which I have for the most part sussed but I have no idea how to show the last part. Electric charge is distributed with variable density $\sigma$ on an infinite plane. $P$ is a point at a distance $a$ from the plane,…
dahaka5
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Help with Derivation of memristor equation

I know this is not the EE stack exchange. I have tried there, no one is replying. Since this revolves around math, and Chua is laying down the mathematical framework for the memristor, I don't believe posting here is too inappropriate. I'm going…
Melendowski
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Plausible correct strategy for approximating the axial and radial components of magnetic induction

Update: After a long struggle, It seems this might just be solving the Laplace equation (zero source coulomb gauge!) in cylindrical coordinates, computing the components of B from $\phi$, and then Taylor expanding. I am revisiting problem 5.4 in…
Kevin Njokom
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Jackson's Book Derivation Of Current Loop Field Error?

In Jackson's book Classical Electrodynamics, 3rd ed., 1999, page 182 there is an integral (I'm editing the original here to keep it short) $$I = \int_0^{2\pi} \dfrac{\cos(\phi') d\phi'}{\sqrt{a^2 + r^2 - 2ar \sin(\theta) \cos(\phi')}} $$ $$ I =…
Researcher720
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Magnitude of current

The current of a germanium diode at room temperature is 100uA at a voltage of -1V. Predict the magnitude of the current for voltages of 0.2V and -0.2V at room temperature. Repeat the prediction for operation at 20°C above room temperature? I had…
user1006899
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Modelling the magnetic field of a conventional tokamak

Recently I have been reading into Nuclear Fusion and the use of spherical tokamaks. My knowledge of maths and physics is quite limited, only a second year undergraduate level. I was wondering how I might obtain equations for the magnetic field…
benmcgloin
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