Lecture 6: Electrostatic Potential

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1 Lectue 6: Electostatic Potential Last lectue eview: Electostatic potential enegy U = F el l efeence point Fo two chages Q an q: U = qe Q l = qq 1 4πε 0 U U ++ o o -+

2 The electostatic potential enegy U() of a chage moving along the -ais is given by: Iclicke Question U() F() Which plot shows the coesponing electostatic foce F() on the chage? 2

3 The electostatic potential enegy U() of a chage moving along the -ais is given by: Iclicke Question U() F() Which plot shows the coesponing electostatic foce F() on the chage? 3

4 Supeposition: seveal inteacting chages Just like electostatic foces an electostatic fiels, electostatic inteaction enegies up: Eample: a positive test chage q 0 inteacting with a (fie) ipole U 0 = q 0q 1 4πε q 0q 2 4πε = q 0q 4πε U 0 +q q 0 q U 0 5

5 Iclicke question q 3 Chage q 3 = q (#3) is bought fom so that this chage an chages q 1 = +q an q 2 = q fom an equilateal tiangle. What is the potential enegy of chage q 3 in the fiel of chages q 1 an q 2? q 1 q 2 A. 0 B. k q2 C. -k q2 D. k 2q2 E. k 2q2 6

6 Iclicke question q 3 Chage q 3 = q (#3) is bought fom so that this chage an chages q 1 = +q an q 2 = q fom an equilateal tiangle. What is the potential enegy of chage q 3 in the fiel of chages q 1 an q 2? q 1 q 2 U 3 = q2 4πε A. 0 B. k q2 C. -k q2 D. k 2q2 E. k 2q2 7

7 Electostatic Potential The electostatic potential V() at any point in space is the electostatic potential enegy that a test chage q woul have at this point, ivie by the test chage q: Electostatic potential (also electic potential ) V = U q Units: J/C=Volt Potential of a point chage Q: Q

8 Fom Electic Potential to Electic Fiel F = U E = V F U = qe = qv Potential of a positive chage V, y = const E =? E, y = const

9 Calculation of Electostatic Potential 1. Discete chages V = k i V = 0 q 2 q i i V q 1 V 2. Continuous chage istibution V = k vol ρ V = 0 τ O 3. E is known V = E l ef.point 10

10 Iclicke Question Compae electostatic potentials at () fo the following chage istibutions: All chage istibutions have the same positive chage ensity λ 12

11 Iclicke Question Compae electostatic potentials at () fo the following chage istibutions: All chage istibutions have the same positive chage ensity λ V = k λl tot R 13

12 Electic Fiel an Potential of a Chage Metal Sphee q=q net - which one shoul we use? Though the (continuous) chage istibution is given, it is easie to use ou esult fo the fiel: V >R = = E l q 4πε 0 2 = = q 4πε 0 V <R =? V <R = q 4πε 0 R 2 q 1 4πε 0 1 = q 4πε 0 14

13 Iclicke question Q Q R Consie two concentic spheical shells, one with aius R an one with aius 2R. Both have the same chage Q. At a point on the oute shell, the magnitue of the electic potential is 2R A. 2kQ/R B. kq/r C. kq/2r D. 0 E. kq/2r 2 15

14 Iclicke question Q Q R Consie two concentic spheical shells, one with aius R an one with aius 2R. Both have the same chage Q. At a point on the oute shell, the magnitue of the electic potential is 2R A. 2kQ/R B. kq/r C. kq/2r D. 0 V = k Q 2R + k Q 2R E. kq/2r 2 16

15 Electic Fiel an Potential of a Paallel-Plate Capacito E E E V V V ef ef

16 Equipotential lines Contou lines on a topogaphic map ae cuves of constant elevation an hence of constant gavitational potential enegy.

17 Equipotential Lines Equipotential lines (an sufaces) ae lines (sufaces) on which the potential (voltage) is constant They ae plotte fo fie iffeences in voltage. +5V 0V -5V -10V -15V At each point, a fiel line is pepenicula to an equipotential line: along equipot. line (suface) E l = 0

18 Dipole Fiel Lines an Equipotential Lines V = +2V V = +1V V = 0V V = 1V 20

19 Iclicke question A +5V 0V -5V Which point coespons to the geatest magnitue of the electic fiel? -10V D B C A. A B. B -15V C. C D. D E, y V, y = V, y y y 21

20 Iclicke question A +5V 0V -5V Which point coespons to the geatest magnitue of the electic fiel? -10V D B C A. A B. B -15V C. C D. D E, y V, y = V, y y y 22

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