1. Electric Potential Physics 102 Professor Lee Carkner Lecture 11

2. PAL #10  Find E 1 and E 2  E 1 = 8.99X10 9 (2X10 -6 )/(3 2 ) = 1124 N /C  r 2 2 = 3 2 + 4 2  r 2 = 5 m  E 2 = 8.99X10 9 (4X10 -6 )/(5 2 ) = 1438 N /C  Find  1 and  2   1 = 0 (right on x-axis)  Can get  2 from triangle  tan  2 = ¾,  2 = 37 degrees   2 is below X axis so is -37 4 m 3 m q 2 = +4  C q 1 = +2  C r 2 =5 m E2E2 E1E1 22 22

3. PAL #10  Find X and Y components  E 1x = E 1 cos  1 = 1124 cos 0 = 1124 N/C  E 1y = E 1 sin  1 = 1124 sin 0 = 0  E 2x = E 2 cos  2 = 1438 cos -37 = 1148 N/C  E 2y = E 2 sin  2 = 1438 cos -37 = - 865 N/C  Find total E vector and angle  E total,x = E 1x + E 2x = 1124 + 1148 = 2272 N/C  E total,y = E 1y + E 2y = 0 – 865 = -865 N/C  E 2 total = E 2 total,x + E 2 total,y  E = (2272 2 +865 2 ) ½  E = 2431 N/C  tan  total = E total,x / E total,y = -865 / 2272   total = -20 degrees  20 degrees below + X axis 4 m 3 m q 2 = +4  C q 1 = +2  C r 2 =5 m E2E2 E1E1 22 22

4. Electrical Potential Energy   The value of the potential tells us how much potential energy is at that point per unit charge  V = PE/q or PE = Vq   1V = 1 J/C   Which could be converted into work or kinetic energy

5. Point Charges and Potential  Consider a point charge Q, what is the potential for the area around it?   At infinity the potential is zero   It can be shown that: V = k e Q / r   Q is charge providing potential, q is charge experiencing potential

6. Finding Potential  If the potential is provided by an arrangement of charges:   Total V = V 1 + V 2 + V 3 …    V = -Ed  We don’t know the potential at anyone point, but we can find the difference between two points separated by a distance d

7. Potential and Energy   The change in energy is:  PE = V f q – V i q = q(V f -V i ) = q  V   PE = -W  Energy could be converted into kinetic energy:  PE =  KE KE i + PE i = KE f + PE f  Particle could speed up or slow down

8. Problem Solving  Particle moving between two points of different potential   Find  V and then  PE (=q  V)   Add or subtract  PE to initial energy of particle

9. Signs  As a positive charge moves with the electric field, the particle gains kinetic energy and loses potential energy   Like dropping a ball in a gravitational field   the electric field does positive work  If a positive charge is forced backwards against an electric field, the particle loses kinetic energy and gains potential energy   like rolling a ball up a hill   the field “does” negative work

10. Potential and Charges  A negative particle:   Opposite of positive particle  A negative particle has the most potential energy at low potential  The potential and the potential energy are two different things   Potential at a point is the same no mater what kind of test charge is put there

11. High potential Low potential

12. Work   Since energy must be conserved:   PE + W = 0 or  PE = -W   Work done by the field is positive if it decreases the potential energy  The “natural” movement   When the charge is forced in the “unnatural” direction  The negative work done by the system is the positive work done on the system

13. E +  Down  gain KE  lose PE  field does +work  “natural”  Up  lose KE  gain PE  you do work  field “does” negative work  “forced”  For negative particle, everything is backwards  But high and low potential are still in the same place High potential Low potential

14. Equipotentials   Each line represents one value of V  Particles moving along an equipotential do not gain or lose energy  Equipotentials cannot cross  Blue = field = E Dashed = potential = V

15. Next Time  Read Ch 17.7-17.9  Homework, Ch 17: P 10, 20, 35, 46

16. Electric Potential Chart sign of  PE sign of  V sign of Wnaturally? + charge moves with E field + charge moves against E field -charge moves with E field -charge moves against E field

17. The above electric field, A)increases to the right B)increases to the left C)increases up D)increases down E)is uniform

18. Is it possible to have a zero electric field on a line connecting two positive charges? A)Yes, at one point on the line B)Yes, along the entire line C)No, the electric field must always be greater than zero D)No, but it would be possible for two negative charges E)No, the electric field is only zero at large distances