a) Find the total electrostatic energy stored in a uniformly charged sphere (not a shell) of...
1. Find the energy stored in a uniformly charged solid sphere of radius R with volume charge density ρ. Do it two different ways: (a) Use the expression for the electrostatic energy in terms of the potential and the charge density, (b) Use the expression for the electrostatic energy in terms of the square of the electric field, 2 Jall space
3. Uniformly Charged Spherical Shell Find the energy of a uniformly charged spherical shell of total charge Q and radius R. (HINT: the relationship V-RdA may be useful, also think about what integrating over dA actually yields)
Find the energy of a uniformly charged solid sphere in the following way: Assemble it like a snowball, layer by layer, each time bringing in an infinitesimal charge dg from far away and smearing it uniformly over the surface, thereby increasing the radius How much work dW does it take to build up the radius by an amount dr? Integrate this to find the work necessary to create the entire sphere of radius R and total charge q.
3) Electrostatic Energy: A sphere of radius A, is charged uniformly with a volume charge density, po. This problem is to be analysed using Gauss's Law. a) State precisely your assumptions regarding the electric field, E, concluded from the symmetries. b) Determine E for r> A |3) Electrostatic Energy: (continued) c) Determine E for 0 <r<A d) Calculate the energy stored in the system. ) Calculate the energy stored in the system
insulating sphere of radius a carries a positive charge 3Q, uniformly distributed its volume. Concentric with this sphere a conducting spherical shell with inner radius b and outer radius c, and having a net charge -Q as shown in Figure. Find the charge distribution on the shell (charge on the inner radius b and charge on the outer radius c) when entire system is in electrostatic equilibrium.
A uniformly charged non-conducting sphere of radius a is placed at the center of a spherical conducting shell of inner radius b and outer radius c. A charge +Q is distributed uniformly throughout the inner sphere. The outer shell has charge -Q. Using Gauss' Law: a) Determine the electric field in the region r< a b) Determine the electric field in the region a < r < b c) Determine the electric field in the region r > c d)...
2. Gauss' Law See Figure 1. A solid, conducting sphere of radius a has total charge (-)2Q uniformly distributed along its surface, where Q is positive. Concentric with this sphere is a charged, conducting spherical shell whose inner and outer radii are b and c, respectively. The total charge on the conducting shell is (-)8Q. Find the electric potential for r < a. Take the potential out at infinity to be 0.
Problem 5. a. Consider a uniformly charged thin-walled right circular cylindrical shell having a total charge Q radius R, and height h. Determine the electric field at a point a distance d from the right side of he cylinder as shown in the figure. a solid cylinder with the same dimensions and carrying the same charge, uniformly ed throughout its volume. Find the electric field it creates at the same point dx
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in Figure P23.46. Suggestion: Use the result of Example 23.8 and treat the cylinder as a collection of ring charges, (b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume....
1.) Consider a spherical shell of radius R uniformly charged with a total charge of -Q. Starting at the surface of the shell going outwards, there is a uniform distribution of positive charge in a space such that the electric field at R+h vanishes, where R>>h. What is the positive charge density? Hint: We can use a binomial expansion approximation to find volume: (R + r)" = R" (1 + rR-')" ~R" (1 + nrR-1) or (R + r)" =R"...