(a) An insulating sphere has radius R and uniform volume charge density ρ. Calculate the electric field at the point P which is inside (r < R) and outside (r > R) of the sphere by using Gauss’s law. Here r is the distance between the center of the sphere and the point P. (b) Discuss the possibility of choosing Gaussian surface other than the sphere. For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric field of a charged sphere? Explain your answer in detail.

(a) An insulating sphere has radius R and uniform volume charge density ρ. Calculate the electric field at the point P which is inside (r < R) and outside (r > R) of the sphere by using Gauss’s law. Here r is the distance between the center of the sphere and the point P. (b) Discuss the possibility of choosing Gaussian surface other than the sphere. For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric field of a charged sphere? Explain your answer in detail.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 22P: Find the electric flux through a rectangular area 3 cm x 2 cm between parallel plates where there is...

See similar textbooks

Similar questions

A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.
The figure here shows a Gaussian cube of face area Aimmersed in a uniform electric field that has the positivedirection of the z axis. In terms of E and A, what is the fluxthrough (a) the front face (which is in the xy plane), (b) therear face, (c) the top face, and (d) the whole cube?
A quarter-disc in the first quadrant has a surface charge density given by K cos φ C/m2. If the radius of the discis b, calculate the electric field at a point P(0, 0, −h
Consider two concentric insulating cylinders of infinite length. The inner cylinder is solid with radius R, while the outer cylinder is a hollow shell with inner radius a and outer radius b. Both cylinders have the same volume charge density of +ρ. Using Gauss’s Law, find the electric field as a function of r (where r= 0 at the central axis) in the interval a≤r < b. Note: Your final equation should be in terms of given parameters of ρ,a,b,R, and r.
If the electric field is given by 6i+3j+4k calculate the electric flux through a surface of area 20 units lying in y-z plane.
A solid insulating plastic sphere of radius a carries atotal net positive charge 3Q uniformly distributed throughout its interior.The insulating sphere is coated with a metallic layer of inner radius a andouter radius 2a. The conducting metallic layer carries a net charge of -2Q. Apply Gauss’s law to find the magnitude of the electric field in the region r < a. Inthe figure, draw the Gaussian surface you are using, and indicate on that surface the direction of anyvectors which appear in the mathematical expression of Gauss’s law. Express your answer in terms ofa, Q, r, and ε0. (If you get an expression involving ρ, substitute it from above to re-express youranswer in terms of the stated variables.)
If the surface charge density on the surface of a conductor, σ = (786 – X) mC/m2 , (where X is your Roll No.). Apply Gauss’ Law to find (with complete logical an mathematical justification): the normal (perpendicular) component of the Electric Field exactly above and below the boundary of the surface if the conductor is placed in free space.
A point charge qq is at the point x=0,y=0,z=0.x=0,y=0,z=0. An imaginary hemispherical surface is made by starting with a spherical surface of radius RR centered on the point x=0,y=0,z=0x=0,y=0,z=0 and cutting off the half in the region z<0.z<0. The normal to this surface points out of the hemisphere, away from its center. Calculate the electric flux through the hemisphere if (a) q=8.00 nCq=8.00 nC and R=0.100 m;R=0.100 m; (b) q=−4.00 nCq=−4.00 nC and R=0.100 m;R=0.100 m; (c) q=−4.00 nCq=−4.00 nC and R=0.200 m;.
A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and Q , respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) ra; (b) arb; and (c) rb.
Is the term in Gauss's law the electric field produced by just the charge inside the Gaussian surface?
Find the electric flux through a rectangular area 3 cm x 2 cm between parallel plates where there is a constant electric field of 30 N/C for the following orientations of the area: (a) parallel to the plates, (b) perpendicular to the plates, and (c) the normal to the area making a 300 angle with the direction of the electric field. Note that this angle can also be given as 180o + 30o.
Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area. What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2? Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.