# Tagged Questions

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### Maxwell equations in cylindrical coordinates [closed]

Give a coil of radius $R$ and $N$ turns crossed by a mean current of $I_0$ ampere at $10 MHz$ frequency (sinusoidal), I need to calculate the behaviour of the electrical and magnetic field inside the ...
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### The fundamental equations of electromagnetism

I'd like to know what are the basic equations of electromagnetism, that can be used to formulate all the other laws and equations. Those basic equations I can think of are Maxwell equations, Lorentz ...
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### E and B field from Time Varying Current

How would I go about calculating the B field and E field from a time varying current charging a capacitor. Theoretically I feel like a solution should exist, but there seems to be a dependence between ...
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### When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of ...
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### Application of Displacement Current

I'm reasonably happy with the derivation and results of displacement current, however, I'd like to be aware of a few practical applications of this idea. So far, the only one I'm aware of is when ...
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### Why is the divergence of a magnetic field equal to zero?

We know due to Maxwell's equations that: $$\vec{\nabla} \cdot \vec{B}=0$$ But if we get far from the magnetic field, shouldn't it be weaker? Shouldn't the divergence of the field be positive? If ...
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### Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
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### Condition for the magnetic field

Let $B$ be the magnetic field. If $$\nabla \times B = 0$$ and of course $$\nabla \cdot B= 0$$ Can we conclude that $B=0$? For a general field it is wrong because every constant vector will ...
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### Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
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### Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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### Maxwell-Faraday Equation and Electric Fields

I have a question regarding, as the title says, this equation: $\nabla \times \textbf{E}=-\frac{\partial \textbf{B}}{\partial{t}}$ So, the above equation says that the curl of an electric field is ...
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### Electromagnetism duality theorem

Concerning Electromagnetism, textbooks often refer to the Duality Theorem. Sometimes it is presented like this: «Consider the Maxwell's Equations (with phasors) and a known field $\mathbf{E}_1$, ...
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### Maxwell's equations of Electromagnetism in 2+1 spacetime dimensions

What would be different in the theory of electromagnetism if instead of considering the equations of Maxwell in 3+1 spacetime dimensions, one would consider 2+1 spacetime dimensions?
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### Which form of Maxwell's equations is fundamental, in integral form or differential form?

I am not sure which form of Maxwell's equations is fundamental, integral form or differential form. Imagine an ideal infinitely long solenoid. When a current is changing in time, can we detect ...
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### What is the physical significance of the Dipole Transformation of Maxwell's Equations?

The Question Given Maxwell's equations of the form \begin{align} \bar{\nabla}\times \bar{B} = \dfrac{4\pi}{c} \bar{J} + \partial_0 \bar{E} \\ \bar{\nabla}\times \bar{E} = -\partial_0 \bar{B} \\ ...
In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...