Laplace equation in spherical coordinates with some symmetry given a sphere with the radius r and the potential on its surface specified by vo k sin2 (1) where k is a constant and 0 is the polar angle. a) which symmetry does the potential obey? calculate the potential inside and outside the sphere the sphere b) calculate the surface charge density o(0) on hints use the ansatz for the symmetry which is derived in the lectures or from griffths chapter 3. use the boundary conditions to simplify the expression, i. e. get rid of some terms compare the coefficients to get the unknown coefficients using the ansatz and the boundary condition

Which lists the main components of darwin’s theory of evolution? a. random mutations drive evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms do not change. b. natural selection drives evolution; the evolution of a population happens slowly; organisms have common ancestors; organisms change over time. c. natural selection drives evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms change over time. d. random mutations drive evolution; the evolution of a population happens rapidly; organisms have common ancestors; organisms do not change.

Astone is dropped with no initial velocity from the top of a cliff and hits the ground a time of 3.9 s later. what is the height of the cliff, in units of meters? you may assume that air resistance is negligible. give the answer as a positive number question 15 a figure skater is rotating at a rate of 200 revolutions per minute. what is the angular speed, in units of rad/s? 200 o 20.9 12000 o 3.33

Two point charges are on the y axis. a 3.90-µc charge is located at y = 1.25 cm, and a -2.4-µc charge is located at y = −1.80 cm. (a) find the total electric potential at the origin. v (b) find the total electric potential at the point whose coordinates are (1.50 cm, 0). v