A point charge q is located at the origin. Consider the electric field flux through a circle a distance 3 μm from 9, subtending an angle 20, where 0 = 30°. The electric flux is equal to A. Find the proportionality constant A in the following cases: E0 a. Calculate the flux through the flat disk bounded by the circle. 0.66 X b. Calculate the flux through the spherical cap (with the sphere centered at the origin) bounded by the circle. 0.66 X

The Electric Field of a Charged Cylinder and a Concentric Cylindrical Shell. A non-conducting cylinder of radius a is charged with charge density p(r) = p.r, where r is the distance from the cylinder axis. The cylinder is placed inside a shell with cylindrical inner and outer radii b and c, respectively. The outer shell is charged with a uniform charge density p(r) = Po. The cylinder and the shell are concentric (see figure). D B b 0 Derive the formulas for the magnitude of the electric field at points A, B, C, and D. Guidance: 1. If required by the formulas, specify Coulomb's force constant through the Vacuum Permittivity, E = 1/4nk instead of Coulomb's onstant, k. 2. Type epso, rhoo, and pi, if the respective symbols Eo,Po, and n, are required.

Imagine that in a region in space you detect a spherical symmetric electric field that increases quadratically with the distance from the center, E (r) = a · r2 . er, where a is a constant. How is the the charge distributed in that region, i.e. find p (r). increases linearly radially outward decreases linearly radially outward uniform

The square surface shown in the figure measures 3.4 mm on each side. It is immersed in a uniform electric field with magnitude E = 1400 N/C and with field lines at an angle of 35° with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface. Normal 4 Number i Units