1 992 Potential difference: (move a charge from initial point i to final point ) F 12 ARED 12 Electric Field due to ring of charge Electric Dipole field along axis of dipole AV = V-V =- E.ds =- [ Ecose ds e is the angle Tastelass ve derived electric field along the axis of a uniformly charged ring: Total charge Q. muulius R: 1 992 U2 == between E and d. 4ac0 712 1 Example from text: Find È at point P at distance z along dipole axis: E = 1 E = E=EI+63+EL Potential energy of the two charges: ATEN T' ARE 1 00 4xEn 7 dq = A ds = À R do Work 0 Work = - F .d? = V =- E-di label diagrun, examine geometry Symmetry: resulting electric field will be along the z axis In this case, we get: E = Ek Electrical Potential of charge q. at point in space a distancer Erway ?? - ???, = jaq components LEt canpol but the poralcl told domiratos. 4 V == 1 4 1 5% = = 1 1 dq AR de Amdz + d ) } V= 4Kg, (+ R) {2 + RF In general, for any E AR: THIS IS EXACT Alternatively, we could do an approximation: If c wd , we are far from dipole compared to its size ... could do an Down tere te -g Electical Polenlial V .Q asr ve E .dà = E cos & dA Electric Field due to Charged Rod ?= Q -- - annravimalian at point P along dipole axis: EXACT for z & R 456622 Example from text: Find Find the electric field due to a charged rod at point P. you'll do another geometric configuration with a charged rod in HW2): Uniformly charged thin red of length L; total charge Q; : charge density A=Q/L. Electric potential of a point charge Magnitude: E 4 4mg,z Find electric potential of charged particle by integrating electric field along path from infinity to distancer from the charge Find the electric field at point P Point Pis a distance r from the charge q. What is the electric potential at point P? Reference: Take V= 0 at r=09 Binomial approximation ( etextbook Appendix E: Binomial Theorem ) P is distance y from the center of the the rod, (in de - A dz Total charge is Q isum up all Ag's) Total length is & (aus tap all &z's) = 21 3 Approximate: (1+x)"" =1-nx for |x| << 1 to ret Then integrate E field from r = co tor = r. Up here the +q Boxs dominates E= N vo)-VO -- -- JE & -- Er Y 4 Tre Are 1 dr =- 1- dr =- e Down hele the -4 E field dominates. 1 144-1+-) Approximation for z> d sum up all the contributiona from Infinitesimal charges Ag At point P, due to symmetry. net E field will only be in the y-direction 1