Physics 2102 Lecture 5

Transcription

1 Physcs 2102 Jonathan Dowlng Physcs 2102 Lecture 5 Electrc Potental I

2 Electrc potental energy Electrc potental energy o a system s equal to mnus the work done by electrostatc orces when buldng the system (assumng charges were ntally nntely separated) U= W The change n potental energy between an ntal and nal conguraton s equal to mnus the work done by the electrostatc orces: ΔU= U U = W What s the potental energy o a sngle charge? What s the potental energy o a dpole? +Q +Q Q a A proton moves rom pont to pont n a unorm electrc eld, as shown. Does the electrc eld do postve or negatve work on the proton? Does the electrc potental energy o the proton ncrease or decrease?

3 Electrc potental Electrc potental derence between two ponts = work per unt charge needed to move a charge between the two ponts: ΔV = V V = W/q = ΔU/q r r dw = F ds r r dw = q E ds 0 r r W = dw = q E ds # # 0 W r r! V = V " V = " = "# E ds q 0

4 Electrc potental energy, electrc potental Unts : [U] = [W]=Joules; [V]=[W/q] = Joules/C= Nm/C= Volts [E]= N/C = Vm 1eV = work needed to move an electron through a potental derence o 1V: W=qΔV = e x 1V = C x 1J/C = J

5 Equpotental suraces W! V = V " V = " = " E r r # ds q Gven a charged system, we can: draw electrc eld lnes: the electrc eld s tangent to the eld lnes draw equpotental suraces: the electrc potental s constant on the surace 0 Equpotental suraces are perpendcular to electrc eld lnes. Why?? No work s needed to move a charge along an equpotental surace. Why?? Electrc eld lnes always pont towards equpotental suraces wth lower potental. Why??

6 Electrc eld lnes and equpotental suraces

7 Electrc potental and electrc potental energy The change n potental energy o a charge q movng rom pont to pont s equal to the work done by the appled orce, whch s equal to mnus the work done by the electrc eld, whch s related to the derence n electrc potental:! U = U " U = Wapp = " W = q! V We move a proton rom pont to pont n a unorm electrc eld, as shown. Does the electrc eld do postve or negatve work on the proton? Does the electrc potental energy o the proton ncrease or decrease? Does our orce do postve or negatve work? Does the proton move to a hgher or lower potental?

8 Example Consder a postve and a negatve charge, reely movng n a unorm electrc eld. True or alse? (a) Postve charge moves to ponts wth lower potental. (b) Negatve charge moves to ponts wth lower potental. (c) Postve charge moves to a lower potental energy poston. (d) Negatve charge moves to a lower potental energy poston (a) True (b) False (c) True (d) True +V Q +Q 0 V

9 Conservatve orces The potental derence between two ponts s ndependent o the path taken to calculate t: electrc orces are conservatve. W! U! V = V " V = " = = " E r r # ds q q 0 0

10 Electrc Potental o a Pont Charge P r r V = " E # ds = " E ds = $ $ R kq kq kq = " dr = + = + $!! 2 r r! R R Note: Q were a negatve charge, V would be negatve

11 Electrc Potental o Many Pont Charges Electrc potental s a SCALAR not a vector. Just calculate the potental due to each ndvdual pont charge, and add together! (Make sure you get the SIGNS correct!) q 4 q 3 r 4 q r 5 5 r 3 P r 2 q 2 r 1 V =! k q r q 1

12 Electrc potental and electrc potental energy! U = Wapp = q! V What s the potental energy o a dpole? +Q Q a Frst brng charge +Q: no work nvolved, no potental energy. The charge +Q has created an electrc potental everywhere, V(r)= kq/r The work needed to brng the charge Q to a dstance a rom the charge +Q s W app =U = ( Q)V = ( Q)(+kQ/a) = kq 2 /a The dpole has a negatve potental energy equal to kq 2 /a: we had to do negatve work to buld the dpole (and the electrc eld dd postve work).

13 Potental Energy o A System o Charges 4 pont charges (each +Q and equal mass) are connected by strngs, ormng a square o sde L I all our strngs suddenly snap, what s the knetc energy o each charge when they are very ar apart? Use conservaton o energy: Fnal knetc energy o all our charges = ntal potental energy stored = energy requred to assemble the system o charges +Q +Q +Q +Q Do ths rom scratch!

14 Potental Energy o A System o No energy needed to brng n rst charge: U 1 =0 Energy needed to brng n 2nd charge: U Charges: Soluton = QV = 2 1 Energy needed to brng n 3rd charge = kq U3 = QV = Q( V1 + V2 ) = + L kq L kq 2 2 Energy needed to brng n 4th charge = 2kQ U 4 = QV = Q( V1 + V2 + V3 ) = + L 2L kq L L +Q +Q +Q +Q Total potental energy s sum o all the ndvdual terms shown 2 on let hand sde = kq L ( 4 + 2) So, nal knetc energy o each 2 charge = kq 4L 2L ( 4 + 2)

15 Summary: Electrc potental: work needed to brng +1C rom nnty; unts V = Volt Electrc potental unquely dened or every pont n space - - ndependent o path! Electrc potental s a scalar add contrbutons rom ndvdual pont charges We calculated the electrc potental produced by a sngle charge: V=kq/r, and by contnuous charge dstrbutons : V= kdq/r Electrc potental energy: work used to buld the system, charge by charge. Use W=qV or each charge.