Capacitor and Electric Potential Energy Analysis
Discover the ease of solving physics problems using energy concepts, illustrated through analyses of a parallel plate capacitor and electric potential energy calculations. Explore the potential energy of point charges and the concept of electric potential across a spherical conductor. Dive into understanding electric potential at different points and the work done on charges in various scenarios.
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Presentation Transcript
Chapter 28 Think back to Ph 211. One of the things we discovered what that many physics problems are much easier if we think in terms of Energy. Consider a Parallel Plate Capacitor E = / 0 Let s use the definition of Work to analyze this situation.
Potential Across a Parallel Plate Capacitor Potential Graph 14 12 10 8 Volts Series1 6 4 2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 Position in x Potential Graph
Potential Across a Parallel Plate Capacitor Electrical Potential Engergy Potential Graph 14 14 12 12 10 10 8 Volts Series1 8 6 Voltage 4 6 2 4 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 S19 2 Position in x S10 position in y 0 S1 25 22 19 16 13 10 7 4 Potential Graph 1 position in x Elevation Graph Equipotential surface Graph S19 S18 S17 12-13 11-12 10-11 9-10 8-9 7-8 6-7 5-6 4-5 3-4 2-3 1-2 0-1 S16 S15 S14 S13 S12 S11 Position in the Y S10 S9 S8 S7 S6 S5 S4 S3 S2 Voltage 27S1 1 3 5 7 9 11 Position in the X 13 15 17 19 21 23 25 Equipotential Surfaces Contour Map
Lets see if we can find the potential energy of a point charge.
If a system contains more than one charge, then the EPE of the system is the sum or the Electric PE of each pair of charge. The Box is 10 Angstroms on edges and the charges are a fundamental unit. PEelectric= k qiqj/rij Find the PE of this system of 4 charges arranged in a box of sizes l and w.: For +3 Exam extra credit points: Create a program that shows the motion of these four charges once you let go of them.
Electric Potential Energy Consider a spherical conductor with a charge of Q=10 C. What would the Electric Potential be at points A and B in the diagram here where rb=1 meter and ra=3meters. Surface A (rA = 3 meters) the potential equals: dev.physicslab.org VA = kQ/r = (9 x 109)(10 x 10-6)/3 = 3 x 104 volts Surface B (rB = 1 meter) the potential equals: VB = kQ/r = (9 x 109)(10 x 10-6)/1 = 9 x 104 volts
If a 2 nC charge were to be brought in from infinity and placed on surface A shown above, the amount of work done on the 2 nC charge would equal 2 x 10-9( V) W = q V = 2 x 10-9(VA - V ) 2 x 10-9(3 x 104 - 0) 6 x 10-5 J We say that the 2 nC charge has gained an electric potential energy of EPEA = 6 x 10-5 J. By definition, the absolute potential at a position infinitely far from a point charge is defined to be zero. Similarly, the amount of work done on the 2 nC charge to bring it in from infinity and place it on surface B would equal 2 x 10-9( V) W = q V = 2 x 10-9(VB - V ) 2 x 10-9(9 x 104 - 0) 1.8 x 10-4 J We say that the 2 nC charge has gained an electric potential energy of EPEB = 1.8 x 10-4 J.
If a system contains more than one charge, then the EPE of the system is the sum or the Electric PE of each pair of charge. Let the size of this molecule be 10 angstroms and have each charge be a fundamental unit of charge. Find the PE of this system.:
What would the E vs. r and V vs. R graphs look like for this case?
We could also create a 3-D potential map of the system. Volts Sy Sx
Or, we could create an equipotential map.
1. Where is the electric field strongest? L, M, N, R, S, T, U 2. Where is the electric field weakest? L, M, N, R, S, T, U 3. What is the direction of the electric field at R? 4. How much work would it take an external agent to move a charge from R to N? 5. What does the negative sign mean in the previous answer?
6. Does it take more work to move a 2 C charge from R to L and then to T compared to going directly to T? 7. How much Potential Energy did the 2 C charge have while it was at rest at position R? 8. What is the 2 C charge s EPE at point T? 9. How much work was required to move the 2 C charge from R to T?
Q You place q a distance R away from Q. What speed does q have when it gets really far away from Q. (q has a mass of m) Q has a length of L. q
29.56 A Uranium nucleus decays via an alpha decay. How fast is a detected alpha particle traveling from a decayed Uranium nucleus? 29.62 Two spherical drops of mercury each have a charge of 0.10 nC and a potential at the surface of 300 Volts. The two drops merge to form a single drop. What is the potential at the surface of the new drop?
