1. Find the energy stored in a uniformly charged solid sphere of radius R with volume...
a) Find the total electrostatic energy stored in a uniformly charged sphere (not a shell) of radius R and charge q. Express your answer in terms of q, R, and constants of nature. There are many different ways to do this, we want you to use both of the following two different methods to check yourself. (i) Figure out E(r) and then use Griffiths Eq. 2.45 shown below (Be careful to integrate over all space, not just where the charge...
Question 22 6 pts A uniformly charged solid insulating sphere of radius R and volume charge density p has an electric field strength inside the sphere (r<R) of E = pr/3£. What is the electric potential inside the sphere? (hint: use the relationship between Vand E. -p/38 p/3E. pr2/6€. pr/380 -pr2/680
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
Consider a solid sphere of radius R = 0.6 m that is uniformly charged with ρ = -16 μC/m3. What is the electric potential a distance 2 m from the center of the sphere?
Consider a solid sphere of radius R = 0.8 m that is uniformly charged with ρ = -10 μC/m3. What is the electric potential a distance 2 m from the center of the sphere?
Consider a solid sphere of radius R = 0.6 m that is uniformly charged with ρ = -10 μC/m3. What is the electric potential a distance 3 m from the center of the sphere?
Consider a solid sphere of radius R 0.4 m that is uniformly charged with ρ- 12 C m, what is the electric potential a distance m from the cente of the sphere?
An insulating sphere with the radius of R = 0.5 meters is uniformly charged so that the volume charge density is ρ = 20 μC/m3. Find the electric field at the point 0.2 meters away from the center of the sphere. Do not include the units in your answers, and round the result to the two significant digits. The electric permittivity of vacuum is ε0 = 8.9×10^−12 C^2/N m^2.
3.) [50 pts] Consider a solid sphere (with radius R) of nonconducting material having a (volume) charge density ρ-ar', where α is a constant (having appropriate units). a.) [10 pts] Provide an expression for the total charge contained in the sphere. b.) [5 pts] Provide an expression for the electric field, Eout, at some position r (relative to the origin at the center of the sphere) located outside the sphere 15pts] Provide an expression for the electric field, Ein, at...
1. Find the electric field at point a for: a. A solid sphere of radius R carrying a volume charge density ρ b. An infinitely long, thin wire carrying a line charge density Side Cross Section C. A plane of infinite area carrying a surface charge density ơ PoT 2. Avery long cylinder with radius a and charge density pa-is placed inside of a conducting cylindrical shell. The cylindrical shell has an inner radius of b and a thickness of...