Question

General Physics II, Phys 2331, Exam Prep 1) Two equal opposite charges are separated from each other with distance d create an electric dipole moment aj Find the electric potential at point A at distance r from the midpoint of two charges (see Fig 1). b) Suppose d <<r find an approximate expression for the electric potential at point A. Hint: use r 2 -2cos 1tax for cos cos ( -0) and (1 t x)" r2 + r2 + COS COS 6 ,r = 1, where r and r are distances between the positive and the negative charges to point A x The magnitude of the electric dipole is p qd. Write you answer from part b in terms of The magnitude of electric dipole p. c 30° and given q Plot the electric potential of the dipole as a function of r for a given 8, for example 0 d) 1 A° e and d and d, for example q Compare the electric potentials of a monopole (a point charge) and a dipole. Plot both of them as e) functions of r. d/2 d/2 r Fig 1: problem (1)

I was able to get about half way through 1 but don't know how to get to cos(cos(theta)). If I can get a step by step force each part that'd be most helpful.

Answer 1

Ansoes Gver thak equa oppost char Seporotd Foom Eoch othes with distanc d creat elechic dipole moment a) tlectricpolential Supeapos tior wil be he at A polen tial o elech the -the Huo changes ( Tt Чтео COSCO)

&uppose der b) then dco se) Y dcose) Y neqlect cose So we Cavat pancing igh bnomial epanha tesms and Cano 음 1J수 o0-1)수 dcoso asujP Sub Sttue case vols + CoSi9 dcose)

c) mode ipol The the pd etechic Hena pcase volk for fuomplu and ds 1 - 31 -4t+9 32 ニ コRXD 3 Y 2 tolt -31 91X the 1 uolG 6 ゆ(1(126u) ( 3,0316) (3,0.l4 0 8 Oxio ol k

Scal but to the Graph S Dot Tbot make Senne e) e tech polerial The monopole go a dipole goe onopou(rdpend clipbl dipclu depercn ndow ux