All Questions
Tagged with electric-fields vector-fields
166 questions
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Why is the oil drop in Milikan's oil drop experiment negative?
I read that the oil drop gains excess electrons while it is between the 2 charged plates, and I found a question which asked this but it has no answer, could someone help me understand why? Thank you
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I can't understand why the divergence of an electric field from a point charge is 0 for points away from the source
I understand that for a positive point charge at the origin, the resulting electric field extends out radially and has magnitude that decreases by $\frac{1}{r^2}$. However, I do not understand why the ...
- 13
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Why is electric field strength indicated by the density of field lines? [duplicate]
It is well known that the magnitude of the electric field is indicated by the density of field lines. However, is it a physical law or additional rule that helps us to draw informative diagrams?
In ...
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Showing surface integral vanishes at infinity - extinction theorem
Suppose the dyadic Green's function $\overline{G}$ is defined as
\begin{equation}
\overline{G}(r, r') = \left(\overline{I} + \frac{\nabla \nabla}{k^2}\right)\frac{e^{-ik\|r - r'\|}}{\|r - r'\|}
\...
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Understanding Gauss' Law with Spherical Symmetry
I've been working on a problem involving the electric field inside a hollow sphere with known inner/outer radii and a volume-charge density $\rho=\frac{k}{r^{2}}$.
I start with Gauss' Law as normal:
$\...
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131
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Can we make field lines for gravity?
I wanted to know if we can draw field lines for the gravitational field
Why I think we should:
Field lines for electrostatics is defined as the path that the positive charge actually undergoes while ...
- 400
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Why many times $E= -{\rm grad} V$ does not give correct direction of the $E$?
Consider a point charge $Q$ at the origin, and consider two points, one on positive $z$ and one on negative $z$ direction, on the positive $z$ direction the point is located at $(0,0,z)$ and on ...
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Method of image charges for ungrounded conductive sphere seems to have charge of $q$ and not $(r/a) q$?
Using the 2d scenario for simplification
Vector field of a point charge $q=1$ at (-4.1,0):
$$\vec F_1\left( {x,y} \right) = \left(\frac{x+4.1} {{\sqrt{(x+4.1)^2 + (y-0)^2}}^2}\right) \vec e_x + \left(\...
- 217
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$\int \vec{E} \cdot \vec{dA} = (E)(A)$?
I've seen this kind of simplification done very frequently in Gauss's law problems, assuming E is only radial and follows some "simple" geometry:
$$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
- 307
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The Curvature of Electric Field Lines
I have been practicing many questions regarding electrical field lines. However, I can't seem to understand when electrical field lines remain straight and when they start to curve. Does it depend on ...
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Accurate drawings of field lines in three situations
I am looking for accurate drawings of the electric and magnetic field lines in three situations:
The electric field lines formed between a positive point charge and negative point charge. (i.e. the ...
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Deriving divergence in cylindrical coordinates, using covariant derivatives
Covariant derivatives are normally used to write equations covariantly in curved spaces. But in an exercise, I need to use covariant derivatives to derive Gauss' law: $\nabla \cdot \vec{E} = 4\pi\rho$ ...
- 145
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149
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In an electrostatic field with zero divergence everywhere, where is the charge located?
Purcell in section 2.17 discusses the electric field $E = <Ky, Kx, 0>$, which has field lines in the shape of a hyperbola, $\phi = -Kxy$, zero curl, and zero divergence. Purcell states that ...
- 309
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What are some ways to derive $\left( \boldsymbol{E}\cdot \boldsymbol{E} \right) \nabla =\frac{1}{2}\nabla \boldsymbol{E}^2$?
For each of the two reference books the constant equations are as follows:
$$
\boldsymbol{E}\times \left( \nabla \times \boldsymbol{E} \right) =-\left( \boldsymbol{E}\cdot \nabla \right) \boldsymbol{E}...
- 105
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Proof for why flux is proportional to number of field lines
What is the proof for this (assuming that we draw infinite field lines).
I understand why flux through some area is proportional to the number of field lines through that area only in the case of an ...
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