Question

The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c In To 2 + y2 where c> 0 is a constant and ro is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c. a. Find the components of the electric field in the x- and y-directions, where E(x,y)= - VV(x,y). Choose the correct answer below. OA. E (x,y) С OB. E Vz+y? (x,y) OC. tolx"+y] «x») cro OD. E= b. Show that the electric field at a point in the xy-plane is directed outward from the origin and has magnitude El = wherer= 1x2 + y2 2 + y Rewrite E in terms of r. Choose the correct answer below. OA. EC Coli OB. E ů OC. EC cro OD. EN Irl?

Answer 1

Uca.in clelt 1242 Tvea, lav -Z au dy - c (uty 2-10 2x fo a? . Cluator - so the 2x ryo ge htye) 12 P x + bc) (x, y) B 2 b E. cr B & E=cr ir1.in Circle 2 E > < 242, (a) a² 32=1 circle. B. t = (-4, xy tangent