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 prese...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge density +ao over the northern hemisphere, and -oo over the southern hemisphere (oo is a positive constant). There are no other charges present inside or outside the sphere. Compute the dipole moment p of this charge distribution assuming the z-axis is the symmetry axis of the distribution. Does p depend on your choice of origin? Why or why not? Are any components of p...
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...
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...
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"...
2) A surface charge density o=0, cos is distributed on a spherical shell of radius R. i) (20 points) Calculate the electric potential outside the sphere using the solution of Laplace equation. ii) (20 points) Find the electric potential using the definition of scalar potential.
Problem 5: A thin (non-conducting) spherical shell of radius R has a uniform surface charge density ơ and is spinning around its axis with angular velocity wWo (a) [3 pts] Find the surface current density K of the spinning shell. (b) [5 pts] Find the magnetic dipole moment m of the spinning shell. Some possibly useful integrals: sin3 θd_ (1/12) (cos(39)-9 cos θ) sin' θd_ (1/32)(129-8 sin(29) + sin(40)) sin2 θ cos2 θdθ = (1/32) (49-sin(49) sin'ecosade = (1/30)cos'(9)(3cos(29-7)