1. (a)Consider a sphere of radius a, with a uniform charge density of unity. Calculate thetotal charge contained by this sphere.(b) Consider now the case of non-uniform distribution of charge with a density functionalform p (r)= K (3-r/a?) for the same sphere. Evaluate the constant K2. (a) Let an electric potential V be independent of x and z, and the gradient of V = 10 y in y-direction. If V = 5 at y = 0, then find V in terms of y.(b) Find the electric field in a region where the plectric potential V = -5 xv

Given: The radius of the sphere is, a. The charge density of the sphere is, ρ=1. The density…

Answered: 1. (a)Consider a sphere of radius a,…

Similar questions

2r 3. Suppose that a sphere of radius 2r and uniform volume charge density p is composed of a nonconducting material (charges remain in placec). A cavity of radius r is then carved out as shown above. Show that the net clectric ficld in the positive +â direction (or any direction for that matter) is given by rp 3€0 E :
I need the answer as soon as possible
An infinite cylinder of radius R has a charge density given by p(r) = ar", where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) 7€or satisfies V ·Ē = 0 for r > R. Explain briefly why this condition must be obeyed.
Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(xOq)/( 2472) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ )(x0 24 We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to…
This is a three part problem. A long nonconducting hollow cylinder of outer radius R and inner radius R/2 has a nonuniform volume charge density of rho(r) = rho-nought(r/R). a) Find the E-field for rR.
A point charge 100 PC is located at (4, l , —3) while the x-axis carries charge 2 nC/m. If the plane z 3 also carries charge 5 nC/m2 , find E at (l, l, l).
A disk of radius R and mass M has a nonuniform surface charge density sigma = Cr, where C is a constant and r is measured from the center of the disk. find the constant c in terms of the mass M and R?
Calculate the electric field at height h above the center of a square plate of size 2a×2a with uniform surface charge density η (both direction and magnitude). Verify that in the limit of large a the result agrees with the field of an infinite uniformly charged plane.
Consider a spherical shell with radius R and surface charge density a= ao cos 0, where is the polar angle in spherical coordinates and the shell is centered at the origin. a) Without computing any integral, argue why is the total charge carried by the shell zero. b) Evaluate the charge carried by the upper hemisphere, in terms of 0.
(a) A particle with charge q is located a distance d from an infinite plane. Determine the electric flux through the plane due to the charged particle. (Use the following as necessary: & and q.) $E, plane = (b) A particle with charge q is located a very small distance from the center of a very large square on the line perpendicular to the square and going through its center. Determine the approximate electric flux through the square due to the charged particle. (Use the following as necessary: & and q.) $E, square= (c) Explain why the answers to parts (a) and (b) are identical.
A ball of conductor of radius RE has total Charge 2Q and a concentric spherical cavity of radius R₁ > RE. At the exact center of the cavity is a charge 3Q. Find the charge q at the radius RE and supply the missing numerical factor below. q=1 Q
Problem 3: UP 6.53 Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E(s) = ps 2€0 PR² 2€ S S≤R SZR

SEE MORE QUESTIONS

1. (a)Consider a sphere of radius a, with a uniform charge density of unity. Calculate the total charge contained by this sphere. (b) Consider now the case of non-uniform distribution of charge with a density functional form p (r)= K (3-r/a²) for the same sphere. Evaluate the constant K