Questions tagged [electromagnetism]

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

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28 views

Image Theory in Electrodynamics

I'm searching for a rigorous mathematical proof of the image theorem for electric/magnetic currents distributions. A proof that, I think, shows that removing the reflecting surface and placing ...
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Mathematical properties of electrodynamic potential

I am faced with a problem that is more mathematical than electrodynamic. However, not having a clearer or shorter title available, I preferred to highlight where the problem came from. However, ...
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Vector Quadruple Product [on hold]

I need to get proof and mathematical expression of the following vector product: AxBxCxD= ? where A,B,C,D all are vectors and I need to get answer of this quadruple vector multiplication. It ...
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Trouble with Stokes' Theorem and the line integral of a piece-wise definition of a continuous curve using polar coordinates.

Problem Statement: Given: $\vec B = (\rho cos \phi)\hat \rho+(sin \phi)\hat \phi$ Verify Stokes' Theorem by evaluating: a) $\oint\limits_c \vec B \bullet d\vec l$, where c represents the closed, ...
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Cycloid motion of charged particle in electromagnetic field

The question is from Schaum's Theoretical Mechanics. The electric field is given by $\underline E=E\hat k$ The magnetic field is given by $\underline B=-B\hat j$ Prove that the motion of a ...
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Triple infinite summation of a 3D Fourier series for Madelung Potential

I'm trying to evaluate the equation below excluding the case when $n_x=n_y=n_z=0$. I know this equation converges everywhere except where x,y, and z are all multiples of $2\pi$. I've attempted ...
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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 ...
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Cross product of unit vector in cylindrical and spherical coordinate system [closed]

For cartesian, the unit vectors are $(ax, ay, az)$ For cylindrical, the unit vectors are $(ar, a\theta, az)$ for spherical, the unit vectors are $(aR, a\theta, a\phi)$ How can one compute cross ...
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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 ...
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Gauss's law in infinite space

Consider an infinite $3$D space with a charge density $\rho$ and a resulting electric field $E$. Imagine $\forall (x,y,z)\in \mathbb{R}^3, \rho(x,y,z) = \rho_0$(a non-zero constant). In this case, ...
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Question on differential equations with $\delta(x)$

In a course of Electrodynamics I came across a function for electric susceptibility $\chi(\tau)$ given by: $$\frac{d^2\chi}{d\tau^2}+\gamma \frac{d\chi}{d\tau}+\omega_0^2\chi=\omega_p^2\delta(\tau)$$ ...
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Binomial series expansion of a trinomial?

In electrostatics, the potential of a charge $q$ placed on the $z$-axis at $z=a$ is \begin{equation} \phi=\frac{1}{4\pi \epsilon_0}\frac{q}{r_1} \end{equation} where $r_1$ is the distance from the ...
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Computing (distributional) gradient of a singular function

This question could well belong better to the physics stackexchange, but I'm hoping that posting it here could give me a more mathematical perspective. I am trying to find the expression for the ...