Questions tagged [gauss-law]

A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.

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Why is the $\vec E$ field inside a sphere = 0? [closed]

I was taught Electric Field inside a sphere is 0, because of Gauss Law. But inside a uniformly charged sphere, if I go at a distance of $r$ from the centre, I will be closer to the +ve charge and ...
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$\nabla. \vec E =\frac{\rho}{\epsilon}$ for a non conservative field

$$\nabla\cdot \vec E =\frac{\rho}{\epsilon}$$ In this formula, suppose I have a non conservative $\vec E$ field, and I put this formula into this expression I will get a corresponding value of $\rho$....
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Electric field inside infinite charged hollow cylinder

Gauss's Law says that electric field inside an infinite hollow cylinder is zero. My question however is that an infinite hollow cylinder can be constructed by taking rings as element and the field ...
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Why charges should go to the surface of conductor? [duplicate]

How can we show that charges should go to the surface of a conductor, assuming that system should minimize its energy? (With no additional assumptions and maybe using variation method!)
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Electric field inside and outside a hollow spherical shell

If a charge(+q) is placed at distance away from a hollow spherical conducting shell , would the net electric field inside the hollow portion remain zero? If the +q charge was placed anywhere inside ...
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Does gravity exist in higher dimensions? [duplicate]

I’m very curious to know whether gravity exists in higher dimensions. Because it follows the inverse square law it seems to me that it should be 3D only (just intuition). Is there any mathematical ...
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What is the electric field between two coaxial conducting cylinders when a charged sphere is placed within the inner cylinder?

A long cylindrical capacitor of length $l$ consists of an outer conductor of radius $a$ and an inner conductor of radius $b$, where $l>>a$. The outer conductor is earthed, and the inner ...
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128 views

Why doesn't shell theorem work here?

I think I have a misunderstanding about the shell theorem regarding electrostatics here. Since we have a conducting spherical shell, and we are looking for the $E$ field, shouldn't it be 0 within ...
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Gauss’s law two concentric cylinders

In the answer key, for part b, they take the charge enclosed to be $Q_{enc} = +\frac{Qh}{L}$ where $h$ is the height of the Gaussian cylinder, $L$ is the length of the cylinder with radius $R_1$, and $...
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About the electric flux at various part of the cube [closed]

A point charge +q is placed at the centre of a cube of side l. What will the electric flux at one of its sides be? How will the flux change if the charge is put on a corner?
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Electric field in capacitor arrangement with different dielectric media

Please consider the following arrangement of infinitely extended charged plates. In z-direction the system also extends to infinity. The charged plate in the middle of the figure is 2x negatively ...
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The electric field of conducting and non conducting sheets

When a non conducting sheet is charged , the electric field due to it is half the electric field due to a charged conducting sheet. How exactly do they differ? When we use gauss law using a Gaussian ...
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Can we use Gaussian pillbox method to determine electric field at a point just near the surface of a surface charge distribution?

I know we can use Gaussian pillbox method to find the discontinuity at the surface of a surface charge distribution. But can we use Gaussian pillbox method to determine electric field at a point just ...
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Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
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Why do my books introduce the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$ without showing partial derivatives of $\mathbf{E}$ exist?

In electromagnetism (electrostatics), we often come across the equation $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$. In order for this equation to be meaningful, $\mathbf{E}$ must be a ...
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Where am I going wrong in deriving Maxwell's first equation in differential form?

By denoting the source coordinates with prime, I get flux through a closed surface: $$\Phi= \displaystyle\oint_{A} \mathbf{E}(x,y,z) \cdot \mathbf{\hat{n}}\ dA =q (x',y',z')$$ And now using the ...
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Why does the electric flux through the surface of a cube with a point charge inside it remain unchanged when the point charge is moved? [closed]

Why does the electric flux inside a cube remain unchanged when the charge is moved within the cube (not on vertices/faces/edges) but just in volume?
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Why isn;t the electric field at all points within concentric metal spheres zero? [closed]

Consider the question: A solid metal sphere of radius a, carrying a charge of +q, is placed inside and concentric with a neutral hollow metal sphere of inner radius b and outer radius c. Determine ...
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What is the physical significance of the complex solutions for the function of electric field inside and outside the solid non-conducting sphere?

Please consider this graph of electric field due to solid non conducting sphere inside and outside the sphere. If we consider the function by its graphical analysis then it is a surjective or many ...
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When to use Poisson's equation in electrostatics

When does when elect to use Laplace's equation when dealing with charge distributions. For example, if I had a metallic sphere of radius $R$ and charge $Q$, then $$\mathbf E = \begin{cases} 0, & ...
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135 views

Why can't Gauss surface be a cube?

For calculating field outside a charged plane conductor, a gaussian surface of Cylinder is considered. I have been said that we consider cylinder because the circle in its upper end is in equal ...
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Volume charge density equation - dimensions not tallying

Write an expression for the volume charge density $\rho(\mathbf{r})$ of a point charge $q$ at $\mathbf{r}'$ in terms of the Dirac delta function. My attempt: Let $\mathbf{r}-\mathbf{r'}=\mathbf{R}$. ...
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Gauss law electric field inside a conductor [closed]

Can you mathematically prove that if there is a cavity in a conductor and no charge is placed in it, the field at all points in the cavity will be zero?
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63 views

Unit conversion between dynes and newtons

I am learning Electricity and Magnetism by myself. Can someone explain me the math behind the equation below? (Quoted from Edward Purcell's Electricity and Magnetism (Cambridge University Press, ...
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Influence of a neutral dielectric on the $\mathbf D$-field

I'm confused with the answer to the following exercise: I don't see how the placement of the sphere would change the $\mathbf D$-field given this arrangement. I think of the $\mathbf D$-field as ...
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On the Electric Field of conductor under Electrostatic Conditions

Let us take a hollow conductor which has a charge Q uniformly distributed on its surface. Now, we know that the Electric field inside the conductor must be ZERO. But what happens when I bring ...
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What is electric field on the surface of a surface charge?

Electric field just near the surface of a surface charge is $\dfrac{\sigma}{2 \epsilon_0} (\hat{n})$ on one side and $-\dfrac{\sigma}{2 \epsilon_0} (\hat{n})$ on the other side. What would be the ...
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Why Electric field inside the spherical shell is zero? [duplicate]

electric field in and out of the spherical shell Why the field inside the conducting spherical shell is zero? Professor Lewin said and I quote," there is NO charge inside the conductor because any ...
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245 views

Point charge inside a hollow conductor, does the exterior field changes when the charge moves?

Suppose that I have a hollow conductor with no specific format. I know that if I put a charge inside it, it will induce charge in the inner surface and on the outer surface a charge with a opposite ...
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Electrostatic in 2D: dimensional analysis

After reading this very interesting post about the electric field and the electric potential of a point charge in 2D and 1D, I've understood that, for the $2D-$case, the following formulas hold: $$ \...
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573 views

What is the electric flux through the flat and curved surfaces? [closed]

My question is from Physics For Scientists And Engineers 7th: A particle with charge Q is located immediately above the center of the flat face of a hemisphere of radius R, as shown in the figure. ...
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316 views

Electric field in center of non-conducting sphere with non-uniform charge distribution from Gauss's law

I'm currently reviewing electricity for the AP Physics C exam, and came across a problem or general topic I don't really understand that has to do with Gauss's law. The general form of Gauss's law we ...
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Why the electric field of an infinity line is dependent on distance? [duplicate]

A very common question about Gauss law is being asked in schools or Internet: Why the electric field of an infinite plane is independent on distance? Actually I was one of who asked this ...
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63 views

Earnshaw's Theorem in Chemical Bonds

Earnshaw's theorem says that: A collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. I also know ...
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Finding electric displacement $\mathbf D$ for a parallel-plate capacitor filled with two slabs of linear dielectric material

This problem refers to Griffiths Problem 4.18: According to my solutions, my lecturer wrote: Only free charge is on plates. $$\mathbf D = -\sigma \hat z \ \text{between the plates and $0$ ...
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Flux received by a negative charge

Consider two charges $+q$ and $-Q$ placed at a distance, note- charge q and Q are different In terms of magnitude. My question: is number of flux lines received by $-Q$ proportional to its own charge,...
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Why is electric field inside a cavity of a non-conducting sphere not zero? [closed]

Consider a charged non conducting solid sphere of uniform charge density, and it as hole of some radius at the centre. Now suppose I apply Gauss law. As there is no charge inside the cavity, no ...
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Calculating flux through a spherical Gaussian sir surface

Three uniformly charged wires with linear charge density $\lambda$ are placed along $x,y$ and $z$. What is the flux of the electric field through Gaussian surface given by $$x^2 + y^2 + z^2 = 1;\, x&...
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Relationship between polarization charge density and free charge density

I have concluded that in a uniform dielectric, volume free charge density $\rho_0$ and volume polarization charge density $\rho'$ satisfy $$ \rho' = \frac{-(\epsilon - \epsilon_0)}{\epsilon}\rho_0 $$ ...
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Principle of superposition in spherical shells

If I have a spherical shell with a uniform positive charge desnity on its surface is near a positive point charge q (sitting in quadrant II area) In consideration of the electric field strength and ...
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113 views

Gauss divergence theorem (GDT) in physics

Some of the statements for $GDT$ which I find in modern textbooks (both electromagnetism and multivariable calculus textbooks) are: (1) Calculus: Several variables Adams Let $D$ be a regular, ...
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element of surface area versus vector element of surface area

In the context of calculating electric flux, is there a difference between element of surface area versus vector element of surface area? Thanks
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Physical example of line charge

Electric field due to an infinite line charge, sheet of charge, point charge, etc are popular problems solved in most text on Gauss's law of electromagnetism. My question: does an (exact or ...
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Why are the two outer charge densities on a system of parallel charged plates identical?

One of the ways examiners torture students is by asking them to calculate charge distributions and potentials for systems of charged parallel plates like this: the ellipsis is meant to indicate any ...
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What is the difference between Closed and Bounded surface?

When I was going through "The Feynman's Lecture on physics" Volume-2 , I found the line "It is useful to speak of the flux not only through a completely closed surface, but through any bounded ...
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529 views

Charged enclosed by the sphere

I'm reviewing the book "Conquering the Physics GRE" for my upcoming Physics GRE. I came across this problem which I'm having trouble with understanding. In particular, I understand the solution that ...
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68 views

Integrating Laplace's equation over a sphere

The Wikipedia page on Laplace's equation states that if the Laplacian of $u$ is integrated over any volume that encloses the source point, $$\iiint_V \nabla \cdot \nabla u \, d^3V =-1.$$ I can'...
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Electrostatics and Gauss law [duplicate]

How can we prove that surface integral of the electric fieldfor a point charge that is outside a gaussian surface, $$\int\mathbf E\cdot\,\mathrm d\mathbf S,$$ without actually using the concept of ...
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Why don't the electric field vectors cancel each other out in a non-conducting infinite plane sheet?

Why do these vectors not cancel each other out in spite of their being in the opposite directions?
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Unstable equilibrium due to an arbitrary electrostatic configuration

Suppose n charges are put in an arbitrary electrostatic configuration and a small test is placed at a null point (i.e., where $\vec{E}=0$ ) of the configuration. The task is to show that the ...