An infinitely long cylindrical conductor has radius R and uniform surface charge density. In terms of R and, what is the charge per unit length for the cylinder?

On a plastic disc of radius R = 10 cm, an electric charge per unit area has been distributed proportional to the distance to the center, the proportionality constant being c = 2 μC/m. Determine the total load of the disk:

An insulating solid spherical shell has inner radius A and outer radius 1.9A. Charge is uniformly distributed throughout the shell with a charge density of +Z. The charge enclosed inside the spherical shell can be written as Q=fZA3 where f is a numerical value with no units. What is the value of f? (Answer should have three significant digits.)

Density, density, density. (a) A charge -328e is uniformly distributed along a circular arc of radius 6.00 cm, which subtends an angle of 72°. What is the linear charge density along the arc? (b) A charge -328e is uniformly distributed over one face of a circular disk of radius 3.50 cm. What is the surface charge density over that face? (c) A charge -328e is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? (d) A charge -328e is uniformly spread through the volume of a sphere of radius 3.30 cm. What is the volume charge density in that sphere? (a) Number Units (b) Number Units (c) Number Units (d) Number Units

An excess positive charge of 6.60 C is transferred to an isolated spherical conductor of radius ?=12.7 cm. What is the volume charge density within the sphere?

Below is a solid sphere of insulating materials (meaning that once placed, charge will not move around even when it feels a force).  This sphere has a changing charge density given by the equation below.  This tells you that there is more charge near the outer edges (when r is larger) then near the center (when r is small) since the charge density is proportional to r^2. In the image R is the total radius of the sphere and r is the distance from the center you will be asked about.  There values are below.  You have to calculate the amount of charge enclosed with the radius of r to find the electric field.  You'll need to integrate to do this - that's where the charge density equation below will be used. Use Gauss's Law to find the Electric Field magnitude at a distance r from the center of the sphere.  Make sure to think about charge enclosed and how to find it.  It is a little more complicated in this problem.  Be careful with your 2 radial values (R and r).

A cylinder of length L=5m has a radius R=2 cm and linear charge density 2=300 µC/m. Although the linear charge density is a constant through the cylinder, the charge density within the cylinder changes with r. Within the cylinder, the charge density of the cylinder varies with radius as a function p( r) =p.r/R. Here R is the radius of the cylinder and R=2 cm and p, is just a constant that you need to determine. b. Find the constant po in terms of R and 2. Then plug in values of R and 1. to find the value for the constant p. c. Assuming that L>>R, use Gauss's law to find out the electric field E inside the cylinder (rR) in terms of 1. and R. d. Based on your result from problem c, find the electric field E at r=1cm and r=4cm.

A disk with radius R and uniform positive charge density o lies horizontally on a tabletop. A small plastic sphere with mass M and positive charge hovers motionless above the center of the disk, suspended by the Coulomb repulsion due to the charged disk. At what height h does the sphere hover? Express your answer in terms of the dimensionless constant v = 20 Mg/ (Qo). Express your answer in terms of some or all of the variables R and v. h = R- 1-v √(2-v)v Submit Part C h = Previous Answers Correct If M = 300 g, Q = 1.0 μC, R = 6.0 cm, and o = 10 nC/cm², what is h? Express your answer with the appropriate units. μᾶ Value 2 Units Submit Previous Answers Request Answer ? <

A cylindrical shell of length l and inner radius a and outer radius b carries a volume charge density given by ρ(r) = α/r where r is the distance to the axis of the shell and α a positive constant. Determine the total charge carried by the shell.

A conductor contains a hollow cavity in which there is a +100 nC point charge. A charged rod transfers -50 nC to the conductor. Afterwards, what is the charge a. On the inner wall of the cavity wall, b. On the exterior surface of the conductor?