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# Gauss' Law

### Gauss's Law: What is the electric flux through a sphere

See attachment for diagram and other information. (a) What is the electric flux through the sphere? (Use r0 for r0, epsilon_0 for 0, and Q as necessary.) (b) What range of values does E have at the surface of the sphere?

### Gauss's Law

(See attachment for diagram and background of this question concerning Gauss' Law) (a) What is the electric field inside the middle sheet? (b) What is the electric field between the left and middle sheets? (c) What is the electric field between the middle and right sheets? (d) What is the charge density on the sur

### Electrostatic field and potential.

I would appreciate help in completing the proof of the equation on the second line of the attached file.

### Coulomb's Law and Electric Field

Three very large square planes of charge are arranged as shown (on edge). From left to right, the planes have charge densities per unit area of -0.50 uC/m^2, +0.10 uC/m^2, and -0.40 uC/m^2. Find the total electric field (direction and magnitude) at the points A, B, C, and D. Assume the plates are much larger than the distance AD

### Proving Gauss Law for arbitrary charge.

Gauss law for arbitray charge distribution is proved in the four part problem. Look at the attached file for details.

### Electrostatics - Gauss's Law, Electrostatic Field due to spherical charge

Hi, This problem is from a book I have, and has three parts. I have attached both the problem (p23.jpg) and the solution (a23.jpg). I've tried different approaches, but I think I'm either not using the correct formula, or not setting up the integrals correctly. I'd appreciate someone showing me how to arrive at the solu

### Spherical Electric Field

A solid insulating sphere of radius R has an electric charge uniformly distributed throughout its volume. The charge per unit volume is p. A) Show that outside the sphere the electric field is given by E = (pR3/3E0r2), where r is the distance from the center of the sphere. B) Show that the field inside the sphere is given by (

### Accuracy of First Order Theory

Problem 20: The finite size of the proton perturbs the energy of the n = 1 orbit in a hydrogen atom. (i) Given the proton to be a uniformly charge sphere of radius R = 1 fm, determine the first order energy shift, making reasonable approximations. How accurate should the first order theory be in this case? (ii) Do the

### A square conducting slab with 10m sides carries a net charge of 10 micro Coulombs. Use Gauss' law to find E inside the slab and close to its surfaces, far from the edges of the slab. The slab is placed to the right of an infinite charged nonconducting plane with charge density of 2 X 10^-6 C/m^2 so that the faces of the slab are parallel to the plane. Find the electric field on each side of the slab far from its edges and the charge density on each face.

A square conducting slab with 10m sides carries a net charge of 10 micro Coulombs. Use Gauss' law to find E inside the slab and close to its surfaces, far from the edges of the slab. The slab is placed to the right of an infinite charged nonconducting plane with charge density of 2 X 10^-6 C/m^2 so that the faces of the sl

### Conductors and Dielectrics

a. A piece of plexiglass (k = 3.2) is placed above an infinite plane of charge with charge density sigma = 0.1 uC/m^2. Compute the bound charge on the bottom surface of the dielectric. Be careful of the sign. b. A material is charged such that the electric field just inside it is 10N/C and is pointed into the boundary. The e

### Electrostatic flux of simple systems.

We learned that the magnitude of the electric field at a point a distance r from an infinite straight wire with a uniformly distributed positive charge E=2k&#955;/r, where &#955; is the charge per unit length on the wire. Imagine that we surround a portion of such a wire with a closed surface shaped like a cylindrical can.

### Use Gauss's Law to find the electic field, electric potential

A solid insulating sphere has a radius A and net charge of +Q. The insulating sphere has a uniform charge density. a conducting sphere of inner radius B and outer radius C surrounds it. I. Use Gauss's Law to find the Electic Field for R<A II. Use Gauss's Law to find the Electic Field for A<R<B III. Use Gauss's Law to fin

### magnitude of electric field near the center of the sheet?

The surface charge density of an infinite sheet of charge is 9.00 X 10^-6 C/M^2. What is the magnitude of electric field near the center of the sheet?

### Uniformly charged field: Calculate capacitance of the coaxial cable arrangement

According to this book, the electric field outside a uniformly charged,infinite cylindrical conductor is the same as if the cylinder's charge were concentrated in a thin wire along the cylinder's axis. Moreover, the potential inside a uniformly charged infinite cylindrical pipe, like that inside a spherical shell, is a constant

### Magnitude of electric field at point just inside outer shell

Consider two concentric spherical shells, one with radius R, and with the radius 2R. Both have the same charge Q. At a point just inside the outershell, the magnitude of the electric field is A. 2kQ/R B. KQ/R C. KQ/2R D. 2kQ/R^2

### Electrostatics and calculation is related to electric field and potential.

A static electric charge is distributed in a spherical shell of inner radius R_1 and outer radius R_2. The electric charge density is given by Rho=a+br, where, r is the distance from the center, and zero everywhere else. (a) Find an expression for the electric field everywhere in terms of r. b) Find expressions for the ele

### Charge density...electric field...electric potential

A (infinitley long) cylindrical non-conducting tube, inner radius a and outer radius b, with charge density p0 sits in a vacuum. Find (show work and derive) and sketch a plot as a function of radius r: A) the charge density B) the total charge enclosed in a cylindrical gaussian surface of radius r C) the electric fie

### Wave Particle Duality and Density

Consider a Gaussian wave packet given by Psi(r)=(1/r) exp(i k.r) where,r=(x^2+y^2+z^2)^(1/2). Calculate the probabilistic current density and interpret the result physically.