Consider a spherically symmetric distribution of charge where the charge density as a function of distance from the center is given by ? (r) = 9.3 r4 x 10-12 C/m3  (note the 10-12 will cancel the 10-12 in ?0).  This charge distribution extends from r = 0 to r = 5.3 m, and beyond that the charge density is 0.  Calculate the magnitude of the electric field r = 8.1 m away from the center of the distribution, in N/C.  Use ?0 = 8.85 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)

Consider a cylindrically symmetric distribution of charge.  It consists of a tube of charge of radius 0.6 m with a linear charge density of 284.8 x 10-12 C/m that is surrounded by a second tube of charge of radius 4.1 m with linear charge density -188.5 x 10-12 C/m.  Calculate the magnitude of the electric field, in N/C, 1.7 m away from the axis of the distribution.  Use ?0ε0 = 8.85 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)

(a) Three point charges are located on the circumference of a circle of radius r, at the angles shown in the figure. 150° O 30° 270⁰ What is the electric field at the center of the circle due to these point charges? (Express your answer in vector form. Use the following as necessary: Ker q, and r.) 3k 3424 (-1) (b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with a minimum separation of 3.90° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum 0.0015 X Epart (a) Place the two charges +q at 0 = 270° ± y, where y is the smallest angle at which the charges do not overlap with the charge -2q, then write an expression for the electric field at the center.

A charge of 7.60 pC is spread uniformly throughout the volume of a sphere of radiusr= 4.15 cm. What is the magnitude of the %3D electric field at a radial distance of (a)6.29 cm and (b)3.23 cm?