Consider an infinitely long cylinder of radius R with two
spherical cavities, also of radius R. The cylinder carries a
uniform volume charge density of ρ. There are two point charges at
the center of the spherical cavities both of charge q.
Hint: Just as the previous hint, superposition is your friend. A
suggestion is to find the contributions from the cylinder and
spheres separately.
(a) Find the electric field at the points A, B, and C in the
diagram below.
(b) Suppose that the point charges have a magnitude q = 4πR3ρ. Find
the energy density of the field outside the cylinder.
Consider an infinitely long cylinder of radius R with two spherical cavities, also of radius R....
Consider an infinitely long straight cylinder of radius R and uniform positive charge density ρ. (a) Find the field inside the cylinder a distance r < R from the center. (b) Find the field outside the cylinder a distance r > R from the center. (c) Sketch a plot of E vs r over the range 0 ≤ r ≤ 2R.
mall portion of an infinitely long cylinder is shown. The radius of the cylinder is R = 4 m and the charge is uniformly distributed throughout the cylinder with a volume charge density of ρ = 0.6 nC/m^3. Gauss's law to find the magnitude of the electric field at a distance r 18 m from the center of the cylinder as shown. Your answer should be in units of N/C. Use Submit Answer Tries /2
Consider an infinitely long, hollow cylinder of radius R with a uniform surface charge density σ. 1. Find the electric field at distance r from the axis, where r < R. (Use any variable or symbol stated above along with the following as necessary: ε0.) 2. What is it for r > R? E(r>R) = ? Sketch E as a function of r, with r going from 0 to 3R. Make sure to label your axes and include scales (i.e.,...
An infinitely long cylinder with axis aloong the z-direction and radius R has a hole of radius a bored parallel to and centered a distance b from the cylinder axis (a+b<R). The charge density is uniform and total charge/length is placed on the cylinder. Find the magnitude and direction of the electric field in the hole.
An infinitely long cylinder of radius R = 3 cm carries a uniform charge density p = 17 Cm. Calculate the electric field at distance r = 18 cm from the axis of the cylinder. Select one: O a. 8.8x10° NC b. 2.8x10NC c. 6.8x103 N/C d. 0.8x10° NIC O O e. 4.8x10 N/C
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p po (a-where po a and b are positive constants and ris the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r< R and (b)r>R
(20 pts) A thick, infinitely long cylinder, with radius R is uniformly charged with volume charge density p. Using Gauss's Law, find the electric field for (a) r < R, and (b) r > R. P R
Consider an infinitely long cylinder with a volume charge density of p(rho) and radius a. Determine the electric field inside the cylinder at r=b (where ba).)>
Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 4.00×10-2 m. The charge density is 6.00×10-2 C/ m3. What is the electric field at r =8.00×10-2 m?
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and a charge per unit length of λ. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume of the cylinder) a) Use Gauss' Law to calculate the electric field at a point outside of the cylinder as a function of r, the radial distance from the center of the cylinder. (r> R) b) Use Gauss'...