### 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.

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

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 divided by 3EOr squared, where r is the distance from the center of the sphere. (b) Show that the field inside the sphere

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 (

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 sl

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=2kλ/r, where λ 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.

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

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?

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

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

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

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.