A law in Classical Electromagnetism and Newtonian Gravity.

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Gauss's law and charge on surface

Consider a cone (not necessarily right cone), with a charge $q$ at its apex. Fix its base, and let the vertex be movable. Now suppose we intend to find the flux through the base. Since the flux ...
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What is the speed of the charge in this setup of spherical conductors? [on hold]

Two concentric spherical conductors respectively have radius $r_1 = 0.145\ \mathrm{m}$ and $r_2 = 0.207\ \mathrm{m}$. The inner sphere carries a charge of $-6.00 \cdot 10^{-8}\ \mathrm{C}$ . An ...
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1answer
4k views

Charge inside conductor

I know that the $E$ field inside a conductor is zero. What happens if I put a source of charge inside the conductor? Say the conductor was spherical centered on the origin and there exists a charge ...
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1answer
40 views

Are $Q1$ and $Q2$ attracted or repelled to the sphere shown in the figure below? [on hold]

Can you tell from the image below if Q1 and Q2 are attracted or repelled. Will Q2 only be attracted to the sphere if Q2 is enough bigger than Q1? Will the positive charge inside the shell attract ...
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45 views

Potential difference inside charge distributions

Always when I think about potential difference inside a symmetrical charge distribution, I think of it being equal to zero because it's dependent on the field and I imagine the directions of each of ...
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Electrostatics question cbse 2015 [on hold]

''The outward electric Flux due to charge +Q is independent of the shape and size of the surface which encloses it.'' Give two reasons to justify this statement.
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A solid non-conducting sphere of radius $R$ carries a non uniform charge distribution [on hold]

A solid non-conducting sphere of radius $R$ carries a non uniform charge distribution with charge density $ ρ = k r/R$, where $k$ is a constant and $r$ is the distance from the center. Show ...
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27 views

Electric Flux through cube [closed]

There is a cube with a charge at one of it's vertex(say A). What is the total electric flux and the flux through each face? I know the answer but not the solution. I don't think gauss law would help ...
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Shell theorem using Gauss Law

Let me present you my problem: Two spherical shells with radius $R_1$ and $R_2$ ($R_1 < R_2$) and masses $M_1$, $M_2$ are concentric. Calculate the gravitational force $\vec{F_g}$ applied ...
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2answers
51 views

Electric field due to a charged conductor

I have this grave confusion that I have been having since a while. When we calculate the electric field due to an infinite plane sheet of charge then the answer comes out to be $σ/2ε$. In this case we ...
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where does the term half in the formula of electrostatic potential energy comes from?(system of point charges)

Electrostatic potential energy stored in a system of point charges (from wikipedia) The electrostatic potential energy $U_E$ stored in a system of N charges q1, q2, ..., qN at positions r1, r2, ...
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Using Gauss's law (differential form) on an infinite line of charge

I just read about Gauss's law in differential form and how to compute divergence. I worked out the $1/r^2$ field and got zero as expected! I was very happy. Then I thought the infinite line of charge, ...
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How can equipotential planes differ in potential in an uniform field?

I'm trying to solve an exercise that asks me the field strength of an uniform electric field where equipotential planes differ by $1\ \mathrm{V}$ and are $2.5\ \mathrm{cm}$ apart. First of all, I ...
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2answers
813 views

Gauss Theorem:Electric field of an uniformly charged non-conducting spherical shell

I want to know the electric field of an uniformly charged non-conducting spherical shell. I know that in case of conductors(metals),the sphere can be shell or it can be solid,but in both the cases ...
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2answers
121 views

Two capacitor plates with equal positive charges $q$

I read in a book that if both the plates of a parallel plate capacitor are given equal positive charges $q$, then the charges on the facing surfaces will be zero and the charge on the outer surfaces ...
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1answer
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Ampere's Law and Gauss's Law for EXACT CENTER of Finite Wire: Mathematical Justification [closed]

I have always seen it explained that: Ampere's Law (in integral form) works whenever B is constant around a path, so that you can pull it out of the integral. Similarly, if you can draw a ...
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1answer
348 views

Apply Gauss' law to find electric field around nonconducting plastic sheets

The question: Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities $\sigma_1$,$\sigma_2$,$\sigma_3$ and $\sigma_4$ on their surfaces, as shown in the ...
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Divergence Theorem, mathematical approach to Gauss's Law?

Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is ...
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2answers
203 views

Why inverse square not inverse cube law? [duplicate]

So as I understand, the inverse-square law which shows up in a variety of physical laws (Newton's universal law of gravitation, Coulomb's law, etc.) is a mathematical consequence of point-like ...
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42 views

Meaning of negative density

Charge density depends on the area/volume and the amount of charge. Before electromagnetism I used to think of density as being positive only. What is the intuitive meaning of negative density? Does ...
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3answers
118 views

Electric field in a conductor

Is it always true that the electric field in a conductor is zero? What would happen if I put a very big charge inside an ungrounded hollow conducting sphere like this image? The charges inside the ...
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2answers
757 views

Why doesn't a gaussian surface pass through discrete charges?

I have read that Gaussian surface cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge ...
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61 views

How to calculate charge on an internal and external surface of a conductor, due to an internal charge

Having a bit of trouble with a question our first year lecturer has given us to think about. Say we're given a hollow cylinder (the hollow region is central and spherical), made of a conducting ...
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69 views

Electric field and flux through a spherical surface inside an uneven hollow charge distribution

Consider a uniformly charged shell and two concentric spherical Gaussian surfaces $S_1$ and $S_2$. ($S_1$ radius is greater than charged shell and $S_2$ radius is less than that of charged shell.) We ...
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Wait… why exactly does farady's ice pail experiment prove Gauss's law?

You'll notice there are no equations in this: that's because this is a question of morale, not of math. But a humble one at that! I come to learn, not to expound. But don't let that limit the form ...
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Electric flux of a closed surface, $\Psi = Q $ or $\Phi =\int\vec{E}\cdot d\vec{A}$

I have problem with the equation of electric flux. I use one book of fundamental physics and another book of electromagnetic engineering; the two of them give different equations for electric flux. ...
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Why we cannot use Gauss's Law to find the Electric Field of a finite-length charged wire?

One of my physics books has a nice example on how to use Gauss's Law to find the electric field of a long (infinite) charged wire. However, at the very end of the example, the author ends by saying ...
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Gauss's Law of Electric Field how it actually works? & How Gauss derived it?

I want to know how Gauss derived his equation of Electric Field. Did he derive it from Coulomb's law? I don't think so. Please tell me some details about how this law works? inside a Gaussian ...
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48 views

What's the geometry of a gravitational field at the flat end of a cylinder?

Gauss's law is fairly straightforward in explaining the gravitational field strength around the curved sides of a cylinder - but what is the geometry of the field at the flat end? For example, does ...
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74 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
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38 views

How to calculate Electric Field near a charged conducting surface without Gauss' law?

I have two problems : In every textbook I find the use of Gauss' law in calculation of Electric Field near a charged conducting surface. Can it be calculated without Gauss' law? Suppose while using ...
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In Gauss's law, why do we use an infinte long wire or long plane to calculate electric field intensity?

In the NCERT textbook of class 12, in the section on applications of Gauss's law, there are three applications. The first application is to calculate the electric field intensity around an infinitely ...
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Inverse Square Law and extra space dimensions

Newton's famous Inverse Square Law says that in $n=3$ dimension of space, force is inversely proportional to the square of the distance between a source and a target. I understand that for higher ...
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How to find the distribution of charge on two spheres connected by a conducting wire?

A solid metal sphere of radius $R$ has charge $+2Q$. A hollow spherical shell of radius $3R$, concentric with the first sphere, has net charge $-Q$. What would be the final distribution of the charge ...
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What does it mean that a magnetic field's flux vanishes through any closed surface?

I'm reading the Britannica guide to Electricity and Magnetism, and I came across the following quote: A fundamental property of a magnetic field is that its flux through any closed surface ...
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Displacement vector in parallel plate capactor

This ought to be simple, but I'm running into some questions... Let's say we have a parallel plate cap with some linear homogeneous dielectric media between the plates. The plates are distance $a$ ...
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1answer
55 views

What do we mean with magnetic monopole and dipole?

What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes. Also,what is their role in ...
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conducting hollow sphere in magnetic monopole

if a hollow copper sphere(or any conducting hollow sphere) is connected to dc at points diametrical and a magnetic monopole is right at the center of the sphere then will there be any movement of the ...
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Potential difference between point on surface and point on axis of uniformly charged cylinder

Question: Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$. Find the potential difference between the surface and the axis of the cylinder. Express ...
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99 views

Flux through plane surface in hemisphere [closed]

Suppose a charge is placed at the centre of a hemispherical surface of radius $R$ then what would be the electric flux passing through the planar surface opposite to the charge in the hemisphere? I ...
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39 views

A flat ring and electrical field

Question: A flat ring (inner radius $R_0$, outer radius $4R_0$) is uniformly charged. In terms of the total charge $Q$, determine the electric field on the axis at points a) $0.25R_0$ ...
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2answers
83 views

Electric field of infinite slab

When reading a book about basic electrodynamics (in a section about electrostatics), I came upon the following problem: An infinite plane slab, of thickness $2d$, carries a uniform volume charge ...
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111 views

Gauss's law and superposition for parallel plates

Two large, flat metal plates are separated by a distance that is very small compared to their height and width. The conductors are given equal but opposite uniform surface charge densities +- ...
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1answer
216 views

Conceptual question on Gauss's Law

By my understanding, the electric field in the surface integral expression for Gauss's Law represents the total electric field and any point on a closed Gaussian surface. However, when we employ ...
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2answers
250 views

Confused about Gauss's Law for parallel plates

I am having trouble understanding Gauss's Law. Suppose we wish to find the electric field strength between two parallel plates with charge density $\sigma$. I know it should be ...
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2answers
155 views

Coulomb's law and Gauss' Law

Which of these laws is more fundamental or forms the basis of electrostatics? I started off with Coulomb's law and then I studied Gauss' law. I was wondering which one is more universal? My professor ...
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Gauss's law for induced electric and magnetic field

Let us consider an accelerating charge, $Q$. As it is accelerating it would radiate energy in the form of EM waves, as per the classical postulates of EM theory. As such there would be induced ...
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Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
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Paradox in electrostatics in relation to Gaussian surfaces?

I have encountered something that is very confusing. My problem is this. I am assuming two infinite cubical Gaussian surfaces sharing a common side. One of the cubes contains a charge $q_1$ at a ...
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81 views

Electric Flux - What is the point?

Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of ...