Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge...
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges present inside or outside the sphere. (a) (4 pts) Compute the dipole moment of that sphere (with the +z-axis up through the pole of the positive, +Oo, hemisphere). Use the definition of a dipole moment, p-Jr, (7)dr', which in this case becomes p:-:J20(7)dA. Write your final answer...
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
Q1. SEPARATION OF VARIABLES - SPHERICAL SIGMA The surface charge density on a sphere (radius R) is a constant, σ0 (As usual, assume V(r = ∞) = 0, and there is no charge anywhere inside or outside, it's ALL on the surface!) i) Using the methods of section 3.3.2 (i.e. explicitly using separation of variables in spherical coordinates), find the electrical potential inside and outside this sphere. ii) Discuss your answer, explain how you might have just "written it down"...
Problem 6: Assume uniform distribution of charge within a sphere with radius R. Determine the total force with which the southern hemisphere acts on the northern hemisphere. Show your solution in terms of radius of the sphere R and the total charge Q. State assumptions if any Problem 6: Assume uniform distribution of charge within a sphere with radius R. Determine the total force with which the southern hemisphere acts on the northern hemisphere. Show your solution in terms of...
A sphere with radius R has charge distribution as given (r,)=k*cos() . Calculate electric dipole moment.(Hint:remember symmetry of charge distribution) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate E(r) B. Use your answer to A to calculate V(r). C. Use your answer to B to calculate the energy of this charge configuration, via the expression U pV d where the integral must be evaluated over the bounded charge distribution. D. Use your answer to A to calculate the energy of this charge configuration, via the expression 2 2 space
You have constructed an arrangement with a nonconducting sphere of radius R inside a thin conducting spherical shell. You have managed to distribute a uniform charge density p inside the nonconducting sphere. Find the electrostatic field inside the nonconducting sphere and outside of the arrangement of sphere and shell. What is the surface charge density on the inner surface of the conducting shell?
1) (a) A conducting sphere of radius R has total charge Q, which is distributed uniformly on its surface. Using Gauss's law, find the electric field at a point outside the sphere at a distance r from its center, i.e. with r > R, and also at a point inside the sphere, i.e. with r < R. (b) A charged rod with length L lies along the z-axis from x= 0 to x = L and has linear charge density λ(x)...
Problem 2: a conducting sphere A conducting sphere has a positive net charge Q and radius R. (Note: since the sphere is conducting all the charge is distributed on its surface.) a) By reflecting on the symmetry of the charge distribution of the system, determine what the E-field lines look like outside the sphere for any r > R. Describe the E-field in words and with a simple sketch. Make sure to also show the direction of the E-field lines....