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.

A law in Classical Electromagnetism and Newtonian Gravity.

Understanding Gauss's law

Classical Electromagnetism

Classical Electricity

Gauss's law for Electricity states that:

$$\nabla\cdot\vec E=\frac{q}{\epsilon_0}$$

Classical Magnetism

Gauss's law for Magnetism states that:

$$\nabla\cdot\vec B=0$$

Newtonian Gravity

Gauss's law for Gravity is simply Poisson's equation

$$\nabla\cdot\vec E=4\pi G\rho$$

1607 questions
83
votes
7 answers

Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?

Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges. Gauss's law implies that the total flux through a surface completely enclosing a charge is…
44
votes
6 answers

Why are so many forces explainable using inverse squares when space is three dimensional?

It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three dimensions and presumably these phenomena have to travel…
39
votes
6 answers

Why does the density of electric field lines make sense, if there is a field line through every point?

When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric field lines, which is inversely proportional to the radius in the case of a single point charge (all field lines are…
30
votes
9 answers

Paradox with Gauss' law when space is uniformly charged everywhere

Consider that space is uniformly charged everywhere, i.e., filled with a uniform charge distribution, $\rho$, everywhere. By symmetry, the electric field is zero everywhere. (If I take any point in space and try to find the electric field at this…
Revo
  • 17,504
29
votes
2 answers

Basis for the Generalization of Physics to a Different Number of Dimensions

I am reading this really interesting book by Zwiebach called "A First Course in String Theory". Therein, he generalizes the laws of electrodynamics to the cases where dimensions are not 3+1. It's an intriguing idea but the way he generalizes seems…
user87745
28
votes
3 answers

What is the electric field in a parallel plate capacitor?

When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is $${\bf E}=\frac{\sigma}{2\epsilon_0}\hat{n.}$$ The factor of two in the denominator comes from the fact that there…
28
votes
5 answers

Using Gauss's law when point charges lie exactly on the Gaussian surface

Suppose you place a point charge $+Q$ at the corner of an imaginary cube. Since electric field lines are radial, there is no flux through the three adjacent (adjacent to the charge) sides of the cube. However there is some amount of flux passing…
28
votes
3 answers

"Find the net force the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere"

This is Griffiths, Introduction to Electrodynamics, 2.43, if you have the book. The problem states Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere. Express your answer in terms of the…
25
votes
3 answers

Field between the plates of a parallel plate capacitor using Gauss's Law

Consider the following parallel plate capacitor made of two plates with equal area $A$ and equal surface charge density $\sigma$: The electric field due to the positive plate is $$\frac{\sigma}{\epsilon_0}$$ And the magnitude of the electric field…
23
votes
4 answers

Divergence of a field and its interpretation

The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. However, clearly a charge is there. So there was no…
19
votes
15 answers

Why is the field inside a conducting shell zero when only external charges are present?

In many introductory books on electrostatics, you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example, if we place an uncharged conducting sphere in a uniform electric field…
Bhavay
  • 1,701
18
votes
2 answers

Gravitational field intensity inside a hollow sphere

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero. What exactly is the reason behind this? Except…
Gummy bears
  • 1,612
17
votes
4 answers

How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?

On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to the surface at a point?
15
votes
4 answers

Divergence of $\frac{ \hat {\bf r}}{r^2} \equiv \frac{{\bf r}}{r^3}$, what is the 'paradox'?

I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2} \equiv \frac{{\bf r}}{r^3}$, now from the book, Griffiths says: Now what is the paradox, exactly? Ignoring any physical…
14
votes
4 answers

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 number of additional plates could be inserted…
1
2 3
99 100