All Questions
Tagged with calculus electric-fields
42
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Equation of infinitesimal ring when finding $ \vec{E}$ of a disc?
When trying to find the electric field created by a uniformly charged disc at a point P on axis of the disc, it can be done by integration.
We start by finding the electric field dE created by each ...
- 799
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The differential of a quantity
I often see the differentials of the electric field strength and the acceleration due to gravity being written as:
$$dE= \mathcal{k}\frac{dQ}{r^2} \tag{1}$$
and
$$dg=\frac{GdM}{r^2} \tag{2}$$
...
- 1,047
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Electric field on the boundary of a continuous charge distribution
In Purcell and Morin's Electricity and Magnetism, 3rd Edition, the claim is made that the magnitude of the electric field on the boundary of a continuous charge distribution is finite (assuming the ...
- 954
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253
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Electric field uniform circle $R$ direction cancel out
I am doing a physics problem involving a uniform circle with a total charge of X, and am attempting to find the electric field on a point charge on the axis of the circle a distance of Z away.
I ...
- 411
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Using Variation of Energy for a Dielectric to define the Electric Field
I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
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How is this possible (electric field integral)?
In the electric field subject, $dq$ is ok to integral. How is this possible? $Q$ is not even changing variable. Can you explain its math?
$$E=k\int \frac{dq}{r^2}.$$
- 13
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Line integral across perfect dipole
In problem 4.7 of Griffiths' "Introduction to electrodynamics, 4th Edition", we are asked to find the potential energy of a dipole in an electric field, $\vec{E}$. In the solution, the ...
- 602
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Why is linear approximation of contribution of electric field the same as if whole charge was concentrated at a single point?
I was reading about electric field of uniformly charged ring, of radius $R$, on the axis of the ring at the distance $d$ from the center of the ring and I am confused about usage of differentials. It ...
- 21
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Electric field of electric dipole and gradient properties
I am trying to work out whether there is a way to calculate the electric field of a dipole from the following formula:
$$\phi(\vec{r}) = -\vec{p} \cdot\vec{\nabla}\phi_0$$
Where $\phi_0$ is the ...
- 309
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Practice Superposing Fields Integral
I've been doing practice problems from Andrew Zangwill's Modern Electrodynamics as I have an exam next week. I am having a bit of difficulty following this integral in the solution's manual:
How do ...
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Why is the electric potential on the surface of a sphere not infinite?
By using Gauss' Law, it can be shown that a uniformly charged hollow sphere can be treated as a point charge lying at its centre with a charge equal to that of the sphere. Owing to this fact, the ...
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In the statement $\text dV = 4\pi x^2\text dx$ , how is the radius $x^2\text dx$?
I was recently studying a question based on Electrostatics. Here is the link to the question (along with the answer below). I haven't learned integration yet. But my question here is how did we get $x^...
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