Questions tagged [electromagnetism]
For questions on Classical Electromagnetism from a mathematical standpoint. This tag should not be the sole tag on a question.
407
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Difficulties employing a line integral of a half circle.
I need to use the following equation (Bio-Savart) of a wire carrying a current, where $d\vec l$ is an infinitesimal piece of wire carrying the charge (the thicker line, half circle)
:
$$d\vec B=\...
- 1,434
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Galilean transformation law for electric and magnetic fields
Under Galilean transformations between a frame A and another frame B in which A is moving with constant velocity $\mathbf V$, a velocity $\mathbf v_A$ is frame $A$ is seen as $$\mathbf v_B = \mathbf ...
- 21
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Finding Im(z) by putting two terms under a common denominator
Sorry if the title is unclear.
I have the following equation for impedance.
$$z=\frac{RiwL}{R+iwL}+\frac{R}{1+iwRC}$$
And I need to find Im(z).
Can I multiply each by its conjugate, and then put ...
- 1,434
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continuity equation involving vectors
A time dependent point charge $q\left ( t \right )$ at the origin $\rho\left ( \vec{r},t \right )=q\left ( t \right )\delta ^{3}\left ( \vec{r} \right ) $, is fed by a current $\vec{J}\left ( \vec{r},...
- 6,343
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Using Line Integrals to solve Amperes Law
I have been reading the forums on how to solve the integral form of ampere's law and I have worked out that the correct way to solve it is to get rid of the dot product by realizing that $|B ∙ dr|$ is ...
- 125
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3k
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infinite square grid of resistors
Given an infinite, 2-d, square grid of 1 Ohm resistors, what is the resistance between two adjacent nodes? (Something like a very large window screen, where the wires have finite resistance, but no ...
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Expanding double angles and simplifying trigonometry
guys I am struggling with the expansion from the second last line to the last for this problem. Any suggestions with examples would be highly appreciated. Thanks a lot
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Solving a 1D integral with system of equations for retarded electromagnetic fields
I need to solve the following integral to calculate the effect of retarded electromagnetic fields on a test charge:
$\int\limits_0^\zeta\frac{(\psi-(1+x)\sin(\psi+\alpha))(\frac{\psi^2}{2\beta^2(1+x)}...
- 21
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Is the reach of the E- and B-field in an EM-wavefront infinite?
In my textbook, the wave-equation for EM waves was derived by using Maxwells' equations in integral form on a EM propgagation in $x$-direction (in vacuum), with E-field in $y$-direction and B-field in ...
- 129
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Dipole-Coupling Tensor: Electrostatic Dipole Moments
I've been struggling with this problem today.
Here's an image of the question I'm attempting to answer.
I'm relatively new to tensor algebra (I've been studying it for about a week or two), and I've ...
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Helmholtz decomposition of a vector field on surface
Does it make sense to do Helmholtz decomposition of a vector field defined on a surface or on a manifold? I am mostly interested in the surface case. I was trying to find a reference for this and ...
- 317
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Numerical algorithm: Spectral function -> Continued Fraction
I am trying to code up a numerical algorithm which takes a spectral function of the form
$$c(\zeta) = w_0 +\sum_{m=1}^N \frac{w_m}{\lambda_m+\zeta}$$
into a continued fraction of the form
$$c(\zeta) = ...
- 591
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How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$
How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$? Is integration the only way?
Homogeneous charge distribution ...
- 1,417
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Calculating the electric field of a disk
I'm having trouble regarding how to calculate the electric field of a disk. Here's the scheme:
The exercise states that the disk is uniformely charged. This is what I did:
Density charge : $\sigma = ...
- 367
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Electrostatic Potential Energy integral in spherical coordinates
I'm having trouble with evaluating an integral that arises from attempting to find the total energy of an electrostatic system consisting of two point charges, which involves an integral over all ...
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