Show that for a charged circular ring of radius a and total charge Q, the electric field anywhere inside the plane of the ring would be zero if the electric field was inversely proportional to r not r2. Your answer is partly verbal and graphical.

Consider a ring of charge.  The ring is in the x-y plane and has a radius of 3.5 m.  The charge per angle as a function of angle α (in radians) around the ring is given by dQ/dα = 6.9 α  (nC/rad). Calculate the z-component of the electric field, in N/C, at the coordinate (0, 0, 9 m).  Use k = 9 x 109 N m2 / C2. (Please answer to the fourth decimal place - i.e 14.3225)

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 ?

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.

A positively charged line with linear charge density λ is pictured along the x-axis with length L. Starting with the differential form of Coulomb’s Law () derive an equation for the electric field at point P at (x=a, y=0) k, a, L, and λ.

Assume you have a line of positive charge with a linear charge density of 10.0 µC/m. Assume that this line of charge is infinitely long and lies on the z-axis (which is perpendicular to both the x- and y-axes). a) Find the strength and direction of the electric field associated with this line of charge at (0.5 m, 0 m, 0 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z b) Find the strength and direction of the electric field associated with this line of charge at (0 m, 0.5 m, 5 m) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z c) Find the strength and direction of the electric field associated with this line of charge at (2.0 m, 0 m, Om) The strength of the field at the stated point is N/C and the direction of the field at the stated point is O-x O+x O-y O+y O-z O+z

There is a +5C charge at the center of a hollow sphere made of a perfect conductor. The hollow sphere has a net charge of +2C, an inner radius of 0.5 m and an outer radius of 0.75 m. Calculate the electric field as a function of distance from the +5C charge and the charge on each surface of the hollow sphere.

Consider a line of charge with a uniform charge density of 35.0 nC/m. It is placed along the line y = − 15.0 cm between the points x = 0 and x = 40.0 cm. Find the electric field vector (both direction and magnitude) due to this line charge distribution at the origin.

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