# 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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### 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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### 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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### How to find surface integral of vector field in cylindrical coordinates through a rectangular plane?

Trying to work through drill problem 3.9 from the 8th edition of the textbook "Engineering Electromagnetics by Hayt". this is the problem question: Given the field D = 6ρ sin(0.5φ) aρ + 1.5ρ cos(0.5φ)...
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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 $$\phi=\frac{1}{4\pi \epsilon_0}\frac{q}{r_1}$$ where $r_1$ is the distance from the ...
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### Can we motivate mathematically why wind turbines almost always have 3 flappers and aeroplane propellers can have any number of flappers?

Firstly I know some might frown upon a question so very broad and applied as this one. It really may not be a well defined mathematical question as some people would prefer on the site. I am okay with ...
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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 ...
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### Apparent paradox when we use the Kelvin–Stokes theorem and there is a time dependency

I am having trouble to understand what is going on with the Maxwell–Faraday equation: $$\nabla \times E = - \frac{\partial B}{\partial t},$$ where $E$ is the electric firld and $B$ the magnetic field. ...
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### Rotationally invariant Green's functions for the three-variable Laplace equation in all known coordinate systems

Green's function for the three-variable Laplace equation in Cartesian coordinates is $$\frac{1}{|\mathbf{r}-\mathbf{r'}|} = \frac{1}{\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}}$$ It may be written in ...
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### finite diference time domain on maxwells equations vs finite difference on magnetic and electric field with wave equations

So I'm just curious you can either write down Maxwell's equations for E and B, or just write wave equations with sources (assuming non zero charge density and current density). With the FDTD you have ...
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### Find the differential equation that the function $f$ must verify in order to respect Maxwell's equations, and the relation between parameters A & B

I'm asked to find the differential equation that $f(\theta)$ must verify in order to respect Maxwell's equations and the relation between parameters $A$ and $B$. They give me this equation for the ...
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### How to integrate Fresnel Integrals? $\int_0^y e^\frac{-j\beta(z)^2}\rho dz$

I am having trouble solving this integration of a spherical fresnel zone with radius y $\displaystyle\int_0^y e^\frac{-j\beta(z)^2}\rho dz$ , where j is complex and $\beta$ and $\rho$ are constants. ...