All Questions
Tagged with electromagnetism surface-integrals
8
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Electric Field felt at the origin of a hemisphere
I want to calculate the Electric Field that is felt at the origin $O$ provoked by a hemisphere of radius $R$ with uniform charge density $\sigma$.
I used spherical coordinates: $\vec{r} = -R(\sin(\phi)...
- 653
2
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1
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126
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What does it mean to say that "$h$ is a coordinate measured normal from the surface"? How does this work in practice?
I am currently studying the textbook Microwave Engineering, fourth edition, by David Pozar. Section Fields at a General Material Interface of chapter 1.3 FIELDS IN MEDIA AND BOUNDARY CONDITIONS says ...
- 4,322
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Flux of the horizontal Electric field through a hemisphere
Suppose I've a hemisphere and an electric field passing horizontally through this hemisphere. I need to find the flux of this field through this hemisphere.
I can easily consider the electric field to ...
2
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Line and Surface Integral with the Dot Product replaced with a Cross Product
Having recently studied magnetostatics, I came across the Biot-Savart law, which is based on the line integal over a current distribution in a curve $C$:
$$\mathbf B(\mathbf r)=\frac{\mu_0}{4\pi}\...
- 109
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641
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Why is the closed line integral used when stating Gauss's law, instead of the closed surface integral?
Sorry if this is nit-picky, but I'm confused as to how to write Gauss's law.
Both my lecturer and this website state Gauss's law as $$\oint\limits_S \vec{E} \cdot d\vec{S} = \frac{q}{\epsilon_0}$$
...
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On using the mean value theorem on this surface integral.
In electrostatics, the surface of a conductor $S$ is always at a constant potential $\phi _{0}$, where the aforementioned potential is a scalar function $\phi (x,y,z)$ defined as :
$$\phi (\textbf{x}...
- 747
4
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Gauss' law and a half-cylinder
The question is:
A half cylinder with the square part on the $xy$-plane, and the length $h$ parallel to the $x$-axis. The position of the center of the square part on the $xy$-plane is $(x,y)=(0,...
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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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