Question

3) A U-shaped rod has vertical sides of length L and a horizontal base of length 2L as shown below. The vertical sides each have a charge per unit length of +A while the base has a charge per unit length of -. Choose a cartesian coordinate system with its origin at the center of the base and with the x- and y- axes horizontal and vertical, respectively a. Solve for the approximate electric potential at the point (0,y) where y>>0. b. Solve for the approximate magnitude of the electric field at the point (x,0) where x>>0. +2 L 2 L Figure 1: Depiction of the geometry for Problem 3.

Answer 1

Questions A u shaped rod has vertical sides of Length I and horizontal bare of Length at as shown below . The vertical side each have a charge ben unit length a while the base has a charge ben unit length of . Choose a Cartension Co-ordinate system with its origin at the centre of the base with the x and y asus horizontal and ventical respectively a) solve the approximate electric potential at two point(0,r) y»o b) solve the approximate magnitude of the elechur hield at the . point (a,0) where you Answer: - a). kt an infinites wall length d² .. . at a distance & from the the axis. We have to find potential at t point þ whose coordinate are (64) 20 the distance from. Infiniteswall zli length in ry-2) +22 I Laza A Now to find the potential and point d due to base ut's taken an infinites mall length dx facon the centree, Potential at due to intinites wall length a TN at Paths due to those within city the time i on korral on An (atkaplaya) 6".. i vos energie en (in the eye)

Potential due to vertical side 90% ma/ly-29TL 10% Amor/lam-7) TEX to whole at point .. So approximate Byscan potential ? We know from Potential dice the to forumila binite length wire . " : &, samoz (sin bhe simon) Ô For verifical side with livean change density a B2.10. Simona Hatua og maling paneb het and for vertical side with linean charge density na By Fo stu ons verby TANGO For base side electric field Ezzo must be zero TIL Febi = ? ano Merbau - (78) antar ê fon 021 Date ante Christmas on Et none on (1) Cond).