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Chapter 25. Electric Potential

Work and Electric Potential Energy
30 mm
-
+
Fe
E
25-1. An positively charged plate is 30 mm above a negatively charged plate, and the electric field intensity has a magnitude of 6 x 104 N/C. How much work is done BY the electric field when a +4-C charge is moved from the negative plate to the positive plate?
Work = Fd = qEd; F opposite to d makeswork negative.
Work = (4 x 10-6 C)(6 x 104 N/C)(0.030 m)
Work = -7.20 x 10-3 J; Work = -7.20 mJ

30 mm
-
+
Fext
E
25-2. In Problem 25-1, how much work is done ON or against the electric field? What is the electric potential energy at the positive plate?
The displacement occurs against the electric force, so that
work done ON the field due to outside UP force Fextin same direction as the displacement.
Since the field is in a position to do positive work when at the positive, plate, the electric potential energy is positive at that point: Ep = +7.20 mJ.

25 mm
-
+
Fe
E
25-3. The electric field intensity between two parallel plates, separated by 25 mm is 8000 N/C. How much work is done BY the electric field in moving a –2-C charge from thenegative plate to the positive plate? What is the work done BY the field in moving the same charge back to the positive plate? (Electric force with motion)
Work done BY field is positive, Fe with displacement.
Work = qEd = (2 x 10-6 C)(8000 N/C)(0.025 m) Work done BY = Loss of electric energy.
Work = 4.00 x 10-4 J Now, in coming back electric force opposes motion.
Workdone BY field is negative: Work = - 4.00 x 10-4 J.
25 mm
-
+
Fe
E
25-4. In Problem 25-3, what is the potential energy when the charge is at (a) the positive plate and (b) the negative plate?
Remember, potential energy represents the work that the
electric field can do when electric forces are free to act. When the –2 C charge is at the positive plate, the E field can do no work,thus with reference to that point, Ep = 0.
(a) At + plate: Ep = 0 No work can be done by the electric field.
(b) At – plate, the field can do +work: Ep = +4.00 x 10-4 J

P
50 mm
±80 C
25-5. What is the potential energy of a +6 nC charge located 50 mm away from a +80-C charge? What is the potential energy if the same charge is 50 mm from a –80-C charge?

P.E. = 86.4 mJ; P.E. = -86.4 mJ

25-6. At what distance from a –7-C charge will a –3-nC charge have a potential energy of 60 mJ? What initial force will the –3-nC charge experience?
; r = 3.15 mm
; F = 19.0 N, repulsion
Note: This value can also be obtained from:

P
40 mm
+12 C
25-7. A +8-nC charge is placed at a point P, 40 mm from a +12-C charge. What is the potential energy perunit charge at point P in joules per coulomb? Will this change if the 8-nC charge is removed?

P.E. = 0.0216 J;
V = 2.70 x 106 J/C ; No The P.E./q is a property of space. If another charge were placed there or if no charge were there, the P.E./q is the same.

25-8. A charge of +6 C is 30 mm away from another charge of 16 C. What is the potential energy of the system?; P.E. = 28.8 J

25-9. In Problem 25-8, what is the change in potential energy if the 6-C charge is moved to a distance of only 5 mm? Is this an increase or decrease in potential energy?
(P.E.)30 = 28.8 J from previous example. Now assume charge is moved.
; (P.E.)5 = 173 J
Change in P.E. = 172. J – 28.8 J; Change = 144 J, increase

25-10. A –3-C charge is placed 6 mmaway from a -9-C charge. What is the potential energy? Is it negative or positive?
; P.E. = +40.5 J
A
8 cm
B
20 cm
-6 C
25-11. What is the change in potential energy when a 3-nC charge is moved from a point 8 cm away from a –6-C charge to a point that is 20 cm away? Is this an increase or decrease of potential energy? (Moves from A to B on figure.)

(P.E.)8 = -2.025 J,...