A charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin 0 cos sin p 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, y) = (a.b.c).

Point P sets above an infinite line of charge 2 m in the positive z direction. The line of charge itself has a charge density ? of -5.0 x 10⁶ C/m. What is the magnitude of the electric field at point P?

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r 1  = 6R  the electric field has a magnitude E 0. What is the magnitude of the electric field at a radial distance r 2 = R/6 as a multiple of E 0 ?

You are working as an intern for a meteorological laboratory. You are out in the field taking measurements with a device that measures electric fields. You measure the electric field in the air immediately above the Earth's surface to be 194 N/C directed downward. (Assume the radius of the Earth is 6.37 x 106 m.) (a) Determine the surface charge density (in C/m²) on the ground. C/m² (b) Imagine the surface charge density is uniform over the planet. Determine the charge (in C) of the whole surface of the Earth. C (c) Determine the Earth's electric potential (in V) due to the charge found in (b). V (d) Determine the difference in potential (in V) between the head and the feet of a person 1.50 m tall. (Ignore any charges in the atmosphere.) V

The volume charge density ρ for a spherical charge distribution of radius R = 6.00 mm is not uniform. (Figure 1) shows ρ as a function of the distance r from the center of the distribution. a)Calculate the electric field at r = 5.00 mm.   b)Calculate the electric field at r = 3.00 mm

Human nerve cells have a net negative charge and the material in the interior of the cell is a good conductor. If a cell has a net charge of -7.52 pC, a. what are the magnitude and direction (inward or outward) of the net flux through the cell boundary? b. what is the volume charge density passing through the cell? Assume that the portion of the cell in question is spherical with radius r 1.2 × 10¯6m.

Electric charge is distributed over the disk a2 + y < 20 so that the charge density at (x,y) is o(x, y) = 5 + x² + y² coulombs per square meter. Find the total charge on the disk.

The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs1.0 m; p(r)= 5p,(1-r/3) For r> 1.0 m; p(r)= 0, where r is in meters. What is the value of r in meters for which the electric field is maximum? O 0.25 O 0.50 О 0.75 O 1.00 O 2.00 О 3.00

Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area.   What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2? Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.

An infinite line charge has constant charge-per-unit-length λ. Surrounding the line charge is a cylindrical shell of radius R, and carrying a constant charge-per-unit area σ. Given λ, what must σ be in order to get 0 electric field for all points outside the cylindrical shell? For that σ, what is the electrical field in between the line of charge and shell?