Johann Carl Friedrich Gauss (; German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] (listen); Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the Princeps mathematicorum (Latin for '"the foremost of mathematicians"') and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians.
This is a general question, I was reading my textbook and this statement confuses me:
"The symmetry of the electric field must match the symmetry of the charge distribution"
this is said regarding symmetry in relation to GAuss' law.
I do not understand what they mean by symmetry of charge...
I have a cube with sides l and therefore a total volume of l^3. The E-field is ax + by + cz where a, b, and c are known constants. It says to find the total E-field. The answer is (a + b + c)*l^3. I have no idea how they get this. I tried summing up all of the sides separately bit I kept getting...
Homework Statement
For the given flux density: \vec{D}=(2y2+z)\widehat{x}+(4xy)\widehat{y}^+(xz)\widehat{z}
a)Determine the charge density.
b)Find the total charge enclosed if the surface is 0<x<1, 0<y<1, 0<z<1 (unit cube)
c)Confirm Gauss’s law by finding the net flux through the surface of...
hi,
im trying to calculate the spectral radius (gauss seidel method) to test whether or not its converges. i no that if the modulus is less than one it converges. however, my answer gives a mixture of solutions which are above and below one - 0.45 and 2.15 and 0. so is this divergent or...
Three large but thin charged sheets are parallel to each other as shown in the figure . Sheet I has a total surface charge density of 7.9 nC/m^2, sheet II a charge of -3.3 nC/m^2, and sheet III a charge of 5.4 nC/m^2.
Figure:
----------------(I)
----------------(II)----------------(III)...
Hi all,
This is just wild shot, since my memory is not what it used to be ...
I remembered reading about Feynman pointing out an interesting
fact, that the integration of the gaussian function
\int_-\infty^\infty e^(-x x) dx = \sqrt[\pi]
has to do with Pi. He then went on to show...
If I have a hypothetical infinite 3 dimensional universe uniformly charged I can argue that the electric field is zero at any given point in space by symmetry. However, if I invoke Gauss' Law I find a non-zero flux of electric field through a gaussian surface encompassing any amount of charge...
Homework Statement
Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge Q1 = -6Q deposited on it. The inner sphere is solid and has a charge Q2 = +1Q on it.
(a) How much charge is on the outer surface?
How much charge is on the inner surface...
Homework Statement
A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ(r) is given by
ρ(r) = 3αr/(2R) for r is less than or equal to R/2
ρ(r) = α[1- (r/R)^2] for R/2 is less than or qual to r which is less than or...
there is a table for standart probility
where we have an integral of exponent in x^2 power
and we can't calculate it so we use a table to get values out of it
where can i find it
?
I don't really know much about serious business electrostatics. I've only taken the AP Physics C E&M exam (using the integral form), but I was looking at wikipedia and I was curious about the differential form of Gauss' Law.
I don't understand what I'm doing wrong with this. I'm trying to...
Homework Statement
Use the divergence theorem to find the outward flux of a vector field
F=\sqrt{x^2+y^2+z^2}(x\hat{i}+y\hat{j}+z\hat{k}) across the boundary of the region 1\leq x^2+y^2+z^2 \leq4
Homework Equations
The Gauss Divergence Theorem states \int_D dV \nabla \bullet...
Homework Statement
I actually just have two questions about the law itself.
1.) Is Gauss's Law just the projection of a shape onto a perpindicular surface to the E field,times the E field?
I ask this because there is an example in my book which shows a 3D incline with a horizontal E...
Homework Statement
A square plate of copper with 50.0-cm sides has no net charge and is placed in a region of uniform electric field of 80.0 kN/C directed perpendicularly to the plate. Find:
(a) the charge density of each face of the plate and
(b) the total charge on each face
Homework...
Hey guys, help needed! Bad lecture, no idea what to do!
The Q1 is:
Q. 1
Three point charges are placed at the apexes of an equilateral triangle as shown in diagram. Calculate the net force on (a) the 5 μC (= 5 × 10‐6 C) charge and (b) the ‐6 μC charge. Give each answer in the form a i + b...
A certain region bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface.
I think it is zero everywhere because as the electric field is entering the closed surface, it...
Gauss' Law only figures out the the total charge enclosed by the Gaussian surface and on it, I treid this in a few cases where charges were placed only inside the surface, and my answers were correct.
But, when I tried imagining how to do this if there were charges present outside...
Homework Statement
The objectives of this exercise is to develop a load flow algorithm based on Gauss Seidel method and then investigate the phenomena of transport of active and reactive power over transmission networks.
Background
A remote load centre is supplied by a remote hydro...
I have read two ideas:
1. is that the 50/ 60Hz everyday home power supplies encourage this
2. that the higher frequencies are disproportionally (greater) 'absorbed' than the lower...
Please point me down the right track
Thank you,
Sem
Homework Statement
A point charge Q is located at the origin. The point charge produces an electric field at a radius of 2.0 meters from the origin of 20N/c.The electric potential of a spherical surface of radius 3.0 meters around the point charge is, in Volts.
Homework Equations...
Hello,
I wonder that the gauss' theorem for gravitational force area.
\int\int_S \vec{g}\hat{n}dS=-4\pi GM=\int\int\int_V \vec{\nabla}\stackrel{\rightarrow}{g}dV
\vec{g}=-G\frac{M}{r^2}\hat{r}\Rightarrow\hat{r}=\frac{\vec{r}}{r}\Rightarrow\vec{g}=-G\frac{M}{r^3}\vec{r}
for...
Hi I'm just making sure I'm understanding the information I'm getting from
"A Student's Guide to Maxwell's Equations"
The book is talking about Gauss' Law for Electric Fields
\bold{E\cdot n}\;\; = E cos (90) = 0
Does this mean that the full electric field is going through the...
Homework Statement
Prove \nabla \bullet E =4 \pi \rho from \partial_{\beta}F^{\alpha \beta}=4 \pi J^{\alpha} where J^{\alpha}=(\rho, J^{1}, J^{2}, J^{3}).
Homework Equations
We are given that F_{\alpha \beta} is
0~~~~E_x~~~E_y~~~E_z
-E_x~~~0~~~~-B_z~~B_y
-E_y~~B_z~~~~0~~~-B_x...
A region in space containing cargo which is distributed spherically so that the stocking load ρ is given by the equotations:
ρ = a for r<=R/2
ρ = 2a(1-r/R) for R/2<=r<=R
ρ=0 for r>=R
The total charge Q is 3*10^-17 C, the radius R of the overall distribution is 2*10^-14 m and a is a constant...
Homework Statement
Non conducting solid cube with a uniform charge distribution. Why is it impossible, or extremely difficult to calculate the field using a larger cube as the gaussian, what about with a sphere as the gaussian?
Homework Equations
gauss' law
The Attempt at a...
Does the magnetic field around a magnet increase when the distance away from the magnet increases? While using a calculator for magnetic flux I noticed that the magnetic flux increases when the air gap increases. So does this mean the magnetic field of a magnet will increase the further you...
Now, i am trying to prove that electric field inside spherical shell whose constant surface charge density \rho is zero. Usually, it is proved by using Gauss law (there is no charge enclosed inside gaussian surface so there is no electric field inside the sphere). But, whe i am trying to solve...
Homework Statement
there are two nonconducting spherical shells fixed in place. shell 1 has uniform surface charge density 6.0 uC/m^2 on its outer surface and radius 3.0cm. shell 2 has uniform surface charge density 4.0 uC/m^2 on its outer surface and radius 2.0cm. the shell centers are...
Homework Statement
Calculate §§ A.n dS if
A= 2y(x^2)i-(y^2)j + 4xzk
over the region in the first octant bounded by (y^2)+(z^2) = 9 and x = 2
Homework Equations
The Attempt at a Solution
Let n = (yj + zk) / 3
then A.n = [-(y^3) +4xz^3] / 3...
Homework Statement
Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...
ok guys.. this question is regarding a spherical nucleus with radius R related to Gauss's Law... so where the electric field given as the following:
E(r) = Q/4*pi*epsilon-nought(r^2+R^2)
1. the questions asks "why this model/behaviour for r>>R might be "reasonable"
2. what q(r) is needed...
An infinite line charge lies on the z-axis with l = 2 µC/m. Coxaial with that line charge are: an infinite conducting shell (with no net charge) with thickness 1 cm and with inner radius 2 cm and outer radius 3 cm, an infinite shell with a radius of 4 cm and with a net charge of -5 µC/m, and...
An infinite line charge lies on the z-axis with l = 2 µC/m. Coxaial with that line charge are: an infinite conducting shell (with no net charge) with thickness 1 cm and with inner radius 2 cm and outer radius 3 cm, an infinite shell with a radius of 4 cm and with a net charge of -5 µC/m, and...
An infinite line charge lies on the z-axis with l = 2 µC/m. Coxaial with that line charge are: an infinite conducting shell (with no net charge) with thickness 1 cm and with inner radius 2 cm and outer radius 3 cm, an infinite shell with a radius of 4 cm and with a net charge of -5 µC/m, and...
I'm reading the book "Electricity and Magnetism: Vol. II" by Edward M. Purcell, in which he describes Gauss' law as stating that the flux through a closed surface is 4π times the enclosed charge (he uses the Centimeter-Gram-Second system).
Later, he refers to Gauss' law as stating that the...
Homework Statement
Use Gauss' law and symmetry to find electrostatic as a function of position for an infinite plane of charge. Let the charge lie in the yz-plane and denote the charge per unit area by \rho=\alpha*e^{-abs(x/b)}
Homework Equations
Q=triple integral of density
The Attempt at...
Homework Statement
A cylinder of length L and radius R is centered on the z-axis in a region where there is a uniform electric field of E i. Determine the flux for the fourth of the cylindrical surface where x > 0 and y > 0.
Homework Equations
\phi = \int E dS
The Attempt at a...
Here's the good explanation.
----------
A surface is an abstract mathematical tool that we can use to explore various phenomena. What a surface is, is a shell around a region of space. Consider a common inflatable ball, such as a soccer ball, or a basketball. The "ball" itself is just a...
I need an explanation that relates the equation to what I learned about the dot product of two vectors being the magnitude of the parallelogram formed by the two vectors in 2D or similarly by the paralleliped formed by three vectors in 3D.
I want to know for instance if the resultant is...
Homework Statement
A long, thin, straight wire of length L has a positive charge Q distributed uniformly along it. Use Gauss' Law to show that the electric field created by this wire at a radial distance r has a magnitude of E = λ/(2πεor), where λ = Q/L. (Hint: For a Gaussian surface, use a...
Hi everybody... I am studying the theory hall sensor for magnetic particle testing...It is a usually techinque non destructive for aeronautic application..In one paper i have read "the hall sensor respose is proportional to the sine of the angle between B and the plane of the hall sensor"..The...
1. The Question
An isolated conductor of arbitrary shape has a net charge of +10\times10^{-6}C. Inside the conductor is a cavity within which is a point charge q = +3\times10^{-6}C. What is the charge on the outer surface of the conductor?
2. The attempt at a solution
On cavity wall...
Two problems one that I have some idea about solving, the other I have no idea at all about where to start.
1. Find the surface integral of E . dS where E is a vector field given;
E = yi - xj + 1/3 z3 and S is the surface x2 + z2 < r2 and 0 < y < b
Well Gauss' theorum would be the place...
Homework Statement
A linear charge lambda = 10^-11 C/m is uniformly distributed along a thin nonconductive rod of length L = 0.5 m.
Use Gauss' Law to calculate the field at a distance of r = 0.1 m from the charged rod.
Homework Equations
∮E.da = Q/ε_0
The Attempt at a Solution
Hi...
Homework Statement
Assuming that an infinitely long line charge of 50(pC/m) parallel to the y-axis at x=2(m) and z=1(m), determine the electric intensity at the point (-1, 5, -3).
The answer given : -0.18(ax0.6 + az0.8)(V/m)Homework Equations
Electric field intensity due to an infinite...
Hello all. I am designing a Gauss jordan elimination program using c++. I need a little help to code this as I am not too familiar with arrays and the operations you can perform on them.
The first question I have is how would I swap rows? I know its probably really simple but I cannot find...
Homework Statement
A 2 C charge is spread uniformly in a hollow sphere with a radius of 50 cm.
a) What is the electric flux?
b) What is the magnitude and direction of an electric field 200 cm away?
Homework Equations
Electric flux = q/(permittivity of free space)
E = q/4(pi)(permittivity...
Is it possible to find the mass of the Earth based on the Earth's volume mass density, roe = A-Br=R, where A = 1.42 x 104 kg/m3, B = 1.16 x 104 kg/m3, and Earth’s radius
R = 6.370 x 106 m
I know that based on Gauss Law that (closed integral) g x da = -4Gmin, where g is the total electric...
Is it possible to find the mass of the Earth based on the Earth's volume mass density, roe = A-Br=R, where A = 1.42 x 104 kg/m3, B = 1.16 x 104 kg/m3, and Earth’s radius
R = 6.370 x 106 m
I know that based on Gauss Law that (closed integral) g x da = -4Gmin, where g is the total electric field...
Homework Statement
Problem 1. A block having mass m and charge +Q is connected to an
insulating spring having force constant k. The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric field of magnitude E directed as shown in Figure
P25:7...