150° 9 270° -2q Q 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 9, and r.) E = 3k q ,.2 -j (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 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.

Problem 3: UP 6.53 Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E(s) = ps 2€0 PR² 2€ S S≤R SZR

can you answer all parts please

Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 2.60R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/2.60 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P? Number i Units (a) (b)

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.