Gauss Definition and 648 Threads

I started having this doubt since i saw the derivation of potential across a capacitor using this method. So.. here i ask: Let there be two large sheets made of insulators, and charged to a planar charge density, \sigma (Sheet 1) and 2\sigma (Sheet 2). Since they are insulators, when placed...

Homework Statement In a spherical region, the voltage is measured to be spherically symmetrical, with v=v(r)=wr^p a. Find the radial electric field. b. Use Gauss’ Law to find the charge enclosed in a sphere of radius r. c. Find the charge enclosed by a sphere of radius...

1 A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q. a) Describe the electric field lines both inside and outside the spheres. b) Use Gauss' law to find an expression for the magnitude of the...

Homework Statement A solid sphere contains a uniform volume charge density (charge Q, radius R). (a) Use Gauss’s law to find the electric field inside the sphere. (b) Integrate E^2 over spherical shells over the volumes inside and outside the sphere. (c) What fraction of the total electrostatic...

! AHH Gauss' Law! Homework Statement Figure 23-27 is a section of a conducting rod of radius R1 = 1.30 mm and length L = 11.00 m inside a thick-walled coaxial conducting cylindrical shell of radius R2 = 10.0R1 and the (same) length L. The net charge on the rod is Q1 = +3.40 × 10^-12 C; that...

the electric field produced due to a time varying magnetic field is non-conservative in nature. does it follow gauss law?

[SOLVED] Gauss and E-Field Homework Statement http://img443.imageshack.us/img443/9452/eletroof9.th.png My main problem with this problem is finding the electric field at Point 2 (P2) Homework Equations The Attempt at a Solution I derived the electric field using Gauss's Law for a...

I'm still not confident with these kinds of problems. Hopefully I got it right, but can someone double check my work? Thanks! Two parallel, infinite planes are separated by a distance d. Find the electric field everywhere (a) if both planes carry a surface charge density \sigma and (b)...

hi, i hav read gauss law chapter from my textbook but still i m facing problems based on it. please explain me GAuss law in an easy language.

Homework Statement What is the escape speed for an electron initially at rest on the surface of a sphere with a radius of 1.0 cm and a uniformly distrubted charge of 1.6 X 10^-15 C? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and...

Homework Statement Consider an infinitely long cylindrical metallic shell with a line of charge within and coincides with the axis of the cylindrical shell as shown in Figure . How does E field vary with r? Homework Equations E.A=q/\epsilon E=E field, A = surface area The...

Homework Statement If the electric field of a point charge were proportional to 1/(r^3) instead of 1/(r^2), would Gauss's law still be valid? Explain reasoning. Homework Equations The Attempt at a Solution Considered a spherical Gaussian surface centered on a single point charge.

I'm reviewing for my final and there is a question I can't seem to solve. If anyone could help me with it I would appreciate it very much. A ruled surface has the parameterization of the form: x(s,t) = A(s) + tB(s) where A(s) is unit speed, |B(s)| = 1. Show that: K<or= to 0. So...

Homework Statement A certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero on the surface? If not, under what circumstances is it zero on the surface? Homework Equations Φ = Qenclosed÷εo = EA The Attempt at a Solution...

Sidney Coleman (1937-2007) was a descendant of Gauss Arivero informed us of this back in 2005, about the time a celebration for the much beloved and admired Sidney Coleman was held at Harvard---the "Sidneyfest". Attended by a who's who of Nobel laureates and the like. Anyway Arivero came up...

I am just interested is there anyway to solve these through a specific method by hand. I know that you can produce an algorithm so that you can solve these into upper triangle form but is there a way to do it by hand other than by inspection.

[SOLVED] Gauss' Law With an Infinite Cylinder of Charge Homework Statement The test question was to find the potential difference between a point S above a cylinder of charger per length lambda, and a point on the surface of the cylinder having radius R and infinite length. Homework...

Homework Statement An insulator in the shape of a spherical shell is shown in cross-section above. (see attached .gif) The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 mC (1 mC = 10-6 C). (You may assume that the charge...

Homework Statement A point charge q_{1} = 4.15 \times 10^-6 is located on the x-axis at x = 1.80 m, and a second point charge q_{2} = -5.80 \times 10^-6 C is on the y-axis at y = 1.10 m. What is the total electric flux due to these two point charges through a spherical surface centered at...

Homework Statement 4. In Fig. 23-28, a butterfly net is in a uniform electric field of magnitude {E = 3.0} mN/C. The rim, a circle of radius a = 11 cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the netting...

Problem Problem 27.56 A sphere of radius R_0 has total charge Q. The volume charge density (C\m^3) within the sphere is \rho(r) = C/(r^2), where C is a constant to be determined. Part A The charge within a small volume dV is dq = \rhodV. The integral of \rhodV over the entire volume of...

Homework Statement An electric field in the region r > a is given by E,r = 2*A*cos(theda)/r^3 E,theda = A*sin(theda)/r^3 E,phi = 0 A = constant Find the volume charge density in this region. E,r and E,theda and E,phi are the components of E in the r, theda, and phi directions...

Two identical conducting spheres each having a radius of 0.460 cm are connected by a light 1.20 m long conducting wire. Determine the tension in the wire if 69.2 (micro)C is placed on one of the conductors. (Hint: Assume that the surface distribution of charge on each sphere is uniform.)...

I'm not entirely sure how to word this without a diagram, but please bare with me! In an ideal case, the charge on a wire is evenly distributed. According to Gauss' Law, an electric field from a charged wire decays with 1/r where r is the distance from the centre of the wire. Say two...

Homework Statement Use Gauss' law to find the charge density on a Van Der Graff dome (r=40cm) if it is charged to 100kV. What is the electric field strength at r=25cm? I understand gauss's law and I know that I need to use it to find the total charge enclosed on the dome. I can then work out...

Homework Statement Is it possible to use Gauss' law to find intensity of a spherical charge distribution where the charge distribution (i)is non-homogeneous in general...i.e. dependent on (r,theta,phi) (ii)can be thought of as a made up of concentric spherical shells of different...

I would appreciate hints on how one can calculate the dependence of the electric potential as a function of distance r from an isolated charge Q in 5-dimensions

Homework Statement Let f be an element of C^2 (R^3=> R) be harmonic in the ball |x|< 1 (i.e. the laplace of f would be 0). Prove that f = 0 inside if it vanishes on the surface |x|=1. What if the dF/dn=0 (partial derivative) on the surface |x|=1 [What is div(f grad f)]? Also think of heat...

hi I have this question, I need your help: If the photon had mass "m" , show that the Gauss' law would no longer be true. Note that the electric poential for a point charge would then have a form V(r) = e/r exp ( -mc/h * r ) Thank you

hi I have this question, I need your help: If the photon had mass "m" , show that the Gauss' law would no longer be true. Note that the electric poential for a point charge would then have a form V(r) = e/r exp ( -mc/h * r ) Thank you

Homework Statement 1.)Two large metal plates of area 1.0m^2 face each other. They are 5 cm apart and have equal but opposite charges on their inner surfaces. If the magnitude E of the electric field between the plates is 55N/C, what is the magnitude of the charge on each plate?Neglect edge...

We have an electric dipole. Now, let us draw a Gaussian surface around our electric dipole. Now, the total charge enclosed by our Gaussian surface is zero, so according the Gauss' Law the flux through the Gaussian surface is zero, and so is the electric field intensity due the electric dipole...

Homework Statement A square plate of edge length 9.0 cm and negligible thickness has a total charge of 6.3 x 10-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm) by assuming that the charge is spread uniformly over the...

I've been reading 'Measuring the World' by D. Kehlmann, i have reached to the part when Gauss using the least square approach (¿? still not 100% sure) discovered the orbit of 'Ceres' but my question is How did he get it??.. assuming the orbit is elliptic and using some possible meditions how...

Hey, I need help to use the Gauss law in this problem: We have A planar slab of charge with a charge density ρv=ρvosin(2*pi/(2*a)),for -a<x<a the thickness of the stab is 2*a. the horizontal y-axis passes through the middle of the stab. the x-axis is vertical a) Find the electric field...

Homework Statement An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density sigma = 12 nC/m^2. The electric field at r = 5.9 cm is approximately a.0.81 kN/C b.zero. c.1.3 kN/C. d.12 kN/C. e.0.56 kN/C...

Homework Statement A sphere of radius 8.0 cm carries a uniform volume charge density rho = 500*10^-9 C/m^3. What is the electric field at r = 3.0 cm? a.36.0 N/C b.230 N/C c.140 N/C d.565 N/C e.450 N/C Homework Equations E = (k*Q*r)/(R^3), where...

Homework Statement A small, insulating, spherical shell with inner radius a and outer radius b is concentric with a larger insulating spherical shell with inner radius c and outer radius d. The inner shell has total charge q distributed uniformly over its volume, and the outer shell has...

Hi, I hope this is advanced enough to warrant being in this section: I'm supposed to use the Gauss theorem (and presumably his law) to show: 1)The charge on a conductor is on the surface. 2)A closed hollow conductor shields its interior from fields due to charges outside, but doesn't...

Please check my work for the following problem: Homework Statement By subsituting A(r) = c \phi(r) in Gauss's and Stokes theorems, where c is an arbitrary constant vector, find these two other "fundamental theorems": a) \int_{\tau} \nabla \phi d \tau = \int_{S} \phi ds b) - \int_{S} \nabla...

Hello, everyone. I hope that you can help me get started on one of the problems I have due this week. Homework Statement Find the electric flux through the hemisphere z = (square root of a^2 - x^2 - y^2). - The Attempt at a Solution I'm fairly certain I need Gauss' law to help...

Homework Statement A charge Q is located inside a rectangular box. The electric flux through each of the six surfaces of the box is: Φ1=+1500 Φ2=+2200 Φ3=+4600 Φ4=-1800 Φ5=-3500 Φ6=-5400. (unit: N x m^2/C) What is Q?Homework Equations ΦE =Q/ε The Attempt at a Solution Add up all the Φ's to...

H e l p m e I want code for gauss elimination by C++ for solving my homework

I have a problem that involves computing the vector surface of z=e^(1-x^2-y^2) where z is greater then or equal to 1, for a Vector Field F=xi+yj+(2-2*z)k. This is to be done using Gauss' theorem. I got an answer of 0, which doesn't seem right I just want to ask if anyone can confirm or deny the...

Ok for example, if a solid conduction sphere was charged to 500volts and had radius of 1cm. Then charge, Q = VR = 5? So the E field just outside the sphere would be E = (1/4pi epsilon) x charge/R^2 = 4.5 x 10^14? Or am i getting confused?

Can anyone help me with how to derive Gauss's law (differential form) from the Divergance theorem?

Hi guys, I am having trouble with this "simple" problem involving these two theorems: Find the value of the integral (A dot da) over the surface s, where A = xi - yj + zk and S is the closed surface defined by the cylinder c^2 = x^2 + y^2. The top and bottom of the cylinder are z= 0 and...

A sphere of radius a has its center at the origin, and has charge density p=Ar^2 another sphere of radius = 2a is concentric with the first. Find the flux SE*da through the larger sphere, where that's the surface integral of E dot da, like usual. It'd just be Qin/e where e is that constant...

A hollow spherical shell carries a charge density \rho = \frac{k}{r^2} in the region a<= r <= b. As in the figure Find the elctric field in these three regions i) r <a ii) a<r<b iii) r>b SOlution: for r<a it simple.. no exclosed charge for any gaussian sphere within that region...

Use Gauss' Law to find the field inside and outside a long hollow cylindrical tube which carries a uniform surface charge sigma. It has been a few months since i did this so i may be a bit rusty As i can recall if there is a point inside a holow cylindrical tube there is no enclosed charge...