All Questions
Tagged with electromagnetism calculus
53
questions
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67
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Solving a funky differential equation.
I'm currently trying to solve the DE that defines charge in a circuit containing an Inductor, Capacitor, Resistor and (crucially) a Memristor. This needs to be able to work for any variable values and ...
- 1
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66
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Calculate Electric Field on the Z-axis from a finite charge wire
I've been trying to find the electric Field on the Z-axis from a non-uniform charge density line charge. The wire is placed on the z-axis from $z=0$ to $z=1$, $E=?$ at $z>1$ and $z<0$
$$
\rho =...
- 1
0
votes
1
answer
55
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I was trying to find field due uniformly charged sheet at a distance h from centre of the square sheet
I assumed the square(side a) sheet to be made up of wires.$$dE=Kdq/r^2$$
The field due to a wire is : Reference
$$\frac{K\lambda}{d}\left[\frac{x}{\sqrt{d^2+x^2}}\right]^{(a/2)}_{(-a/2)}=\frac{K\...
- 471
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63
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Electric field flux proportional to the field lines generated by (for example) a static charge
Suppose we have a stationary positive charge at a point in space that we call $+Q$. We know by definition that the flow of the electrostatic field is given by, in its simplified form,
$$\Phi_S(\vec E)=...
- 7,792
1
vote
1
answer
93
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Distance becoming equal to displacement
Consider a charged particle of charge q and mass m being projected from the origin with a velocity u in a region of uniform magnetic field $\mathbf{B} = - B \hat{\mathbf{k}} $ with a resistive force ...
- 333
2
votes
2
answers
251
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Why can't math software solve the integral $\int\limits_{-a/2}^{a/2}\int\limits_{-a/2}^{a/2}\frac{1}{\sqrt{x^2+y^2+z^2}}dxdy$?
Consider the task of finding the electric field at a height $z$ above the center of a square sheet of side a carrying uniform charge $\sigma$.
I am asking this in the math stack exchange because ...
- 5,021
3
votes
1
answer
79
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vector calculus directions
Consider a current density:
$$\vec{j}=j_0(1-\frac{r^2}{R^2})\vec{e_3}$$ if $r\le R$ and $j=0$ if $r\ge R$
where $r$ is the distance from the $x_3$ axis.
I need to use Biot-Savart law to find the ...
- 429
1
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0
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21
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Multipole expansion - shaky calculus foundation please have a look
Calculate the leading behavior of the electrostatic potential $V(x)$ at large distances $|x| ≫ a$ for the following charge distributions:
a) One charge $q$ at the point $x_0 = ae_x$ and one charge $q$ ...
- 429
1
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0
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60
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Huygens' principle for diffraction through an apeture
I understand that integrals are analogous to summing for continuous values, but for some reason I am still terrible at modeling continuous phenomena. Take for example calculating the diffraction of a ...
- 613
1
vote
1
answer
52
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Deriving Fresnel diffraction from Huygen's principle
I am following the book Introduction to Infrared and Electro-Optical Systems by Driggers. Below is a derivation of Fresnel diffraction using Huygen's principle. In (4.24), the $t$ should be a $z$
...
- 613
4
votes
1
answer
158
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Properties about an elliptic integral of the first kind.
In polar coordinates, the electric potential of a ring is represented by the next relation
$$
\frac{\lambda}{4\pi\varepsilon_0}\frac{2R}{|r-R|}\left( F\left(\pi -\frac{\theta}{2}\Big|-\frac{4 r R}{(r-...
- 51
-2
votes
1
answer
93
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calculating curl
With
$$\tilde{\mathbf{E}}=2j\hat{y}E_me^{-jk_zz}\sin(k_xx)\quad\text{for}\quad 0<x<a$$
the phasor form of Faraday's law $\nabla\times\tilde{\mathbf{E}}=-j\omega\mu_0\tilde{\mathbf{H}}$ leads to
$...
- 29
0
votes
2
answers
61
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What math technique is used to get $k\left(\sqrt{r_o^2+x^2}-r_o\right) \approx kr_o \left(1+\frac12 \frac{x^2}{r_o^2}-1\right)$? [closed]
How is this equation in left-hand side, approximately equal to the right hand side? What math technique is used?
$$k\left(\sqrt{r_o^2+x^2}-r_o\right) \approx kr_o \left(1+\frac12 \frac{x^2}{r_o^2}-1\...
- 29
6
votes
2
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227
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Understanding if the integral expression obtained is correct and if its (incorrect ) mistake in the approach to get that result
The integral was:
$$\int_{0}^{\frac{\pi}{2}} \frac{\cos^2x}{(a^2+b^2\sin^2x)^{3/2}}\;dx= \frac{\pi}{2ab^2} (1-\frac{a}{\sqrt{a^2+b^2}}).$$
I encountered this integral while trying to show amperes ...
- 977
1
vote
4
answers
435
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Proof that $\nabla \times E = 0$ using Stokes's theorem
Firstly, I know that this can be proved by showing the curl of a gradient is $0$. I am not interested in that. I am interested in the validity of using Stokes's theorem. One way that Jackson proves ...
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