Electric Potential. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

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1 Electic Potential A PowePoint Pesentation by Paul E. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 2007

2 Objectives: Afte completing this module, you should be able to: Undestand an apply the concepts of electic potential enegy, electic potential, and electic potential diffeence. Calculate the wok equied to move a known chage fom one point to anothe in an electic field ceated by point chages. Wite and apply elationships between the electic field, potential diffeence, and plate sepaation fo paallel plates of equal and opposite chage.

3 Review: Wok and Enegy Wok is is defined as as the poduct of of displacement d and a paallel applied foce F. F. Wok = Fd; Units: 1 J = 1 N m Potential Enegy U is is defined as as the ability to to do wok by vitue of of position o o condition. (Joules) Kinetic Enegy K is is defined as as the ability to to do wok by vitue of of motion (velocity). (Also in in joules)

4 Signs fo Wok and Enegy Wok (Fd) is is positive if if an applied foce F is is in in the same diection as as the displacement d. d. B F m mg A d The foce F does positive wok. The foce mg does negative wok. The P.E. at B elative to A is positive because the field can do positive wok if m is eleased. P.E. at A elative to B is negative; outside foce needed to move m.

5 Gavitational Wok and Enegy Conside wok against g to move m fom A to B, a vetical height h. Wok = Fh = mgh At level B, the potential enegy U is: U = mgh (gavitational) The extenal foce does positive wok; the gavity g does negative wok. B F m mg A h g The extenal foce F against the g-field inceases the potential enegy. If If eleased the field gives wok back.

6 Electical Wok and Enegy An extenal foce F moves +q fom A to B against the field foce qe. Wok = Fd = (qe)d At level B, the potential enegy U is: U = qed (Electical) The E-field does negative wok; Extenal foce does positive wok. B F e +q + d qe E A The extenal foce F against the E-field inceases the potential enegy. If If eleased the field gives wok back.

7 Wok and Negative Chages Suppose a negative chage q is moved against E fom A to B. Wok by E = qed At A, the potential enegy U is: U = qed (Electical) No extenal foce is equied! B qe -q A d E The E-field does positive wok on q deceasing the potential enegy. If If eleased fom B nothing happens.

8 Wok to Move a Chage + + Q b F a Avg. Foce: F avg kqq kqq Wok Fd ( a b) a b a b qe Wok to move +q fom A to B. At A: At B: F a F Distance: a - b b kqq 2 a kqq Wok kqq b a b

9 Absolute Potential Enegy + + Q b a 1 1 Wok kqq b a Absolute Potential Enegy: Absolute P.E. is elative to F It is wok to bing qe +q fom infinity to point nea Q i.e., fom to b 1 1 kqq Wok kqq 0 b b U kqq

10 Example 1. What is the potential enegy if a +2 nc chage moves fom to point A, 8 cm away fom a +6 C chage? The P.E. will be positive at point A,, because the field can do + wok if q is eleased. Potential Enegy: U U kqq A +Q +6 C 9 Nm C +2 nc (9 x 10 )( 6 x 10 C)(+2 x 10 C) (0.08 m) 8 cm U = 1.35 mj Positive potential enegy

11 Signs fo Potential Enegy Conside Points A, B, and C. Fo +2 nc at A: U = mj Questions: If +2 nc moves fom A to B, does field E do + o wok? Does P.E. incease o decease? A 8 cm +Q +6 C Moving positive q 4 cm C B 12 cm +2 nc The field E does positive wok, the P.E. deceases. If +2 nc moves fom A to C (close to +Q), the field E does negative wok and P.E. inceases.

12 Example 2. What is the change in potential enegy if a +2 nc chage moves fom to B? Potential Enegy: kqq U Fom Ex-1: U A = mj A 8 cm +Q +6 C B 12 cm U B (9 x 19 )( 6 x 10 C)(+2 x 10 C) 9 Nm C (0.12 m) U = U B U A = 0.9 mj 1.35 mj mj U = mj Note that P.E. has deceased as wok is done by E.

13 Moving a Negative Chage Conside Points A, B, and C. Suppose a negative -q q is moved. Questions: If -q moves fom A to B, does field E do + o wok? Does P.E. incease o decease? A 8 cm +Q +6 C 4 cm C B 12 cm Moving negative q - The field E does negative wok, the P.E. inceases. What happens if we move a 2 nc chage fom A to B instead of a +2 nc chage. This example follows...

14 Example 3. What is the change in potential enegy if a -22 nc chage moves fom to B? Potential Enegy: U kqq Fom Ex-1: U A = mj (Negative due to chage) (9 x 19 )(6 x 10 C)(-2 x 10 C) 9 Nm C U B (0.12 m) U B U A = -0.9 mj (-1.35 mj) A 8 cm +Q +6 C B 12 cm mj U = mj A chage moved away fom a + chage gains P.E.

15 Popeties of Space Electic Field. E + + Q E is a Vecto An electic field is a popety of space allowing pediction of the foce on a chage at that point. F E ; F qe q The field E exist independently of the chage q and is found fom: Electic Field : E kq 2

16 Electic Potential Electic potential is anothe popety of space allowing us to pedict the P.E. of any chage q at a point. Electic Potential: U V ; U qv q The units ae: joules pe coulomb (J/C) U P. V q + + Q Potential Fo example, if the potential is 400 J/C at point P, a 22 nc chage at that point would have P.E. : U = qv = (-2 x 10-9 C)(400 J/C); U = -800 nj nj

17 The SI Unit of Potential (Volt) Fom the definition of electic potential as P.E. pe unit chage,, we see that the unit must be J/C.. We edefine this unit as the volt (V). V U 1 joule ; 1 volt = q 1 coulomb A potential of of one volt at at a given point means that a chage of of one coulomb placed at at that point will expeience a potential enegy of of one joule.

18 Calculating Electic Potential Electic Potential Enegy and Potential: U kqq Substituting fo U, we find V: ; V V U q kqq q kq kq P. V + + Q Potential V kq The potential due to to a positive chage is is positive; The potential due to to a negative chage is is positive. (Use sign of of chage.)

19 Example 4: Find the potential at a distance of 6 cm fom a 55 nc chage. P. q = 4 C 6 cm Q Q = -5 nc V kq Negative V at Point P : x 10 Nm 2 ( 5 x 10 C) C (0.06 m) V P = -750 V What would be the P.E. of a 4 C chage placed at this point P? U = qv = (-4( 4 x 10-6 C)( C)(-750 V); U = 3.00 mj Since P.E. is is positive, E will do + wok if if q is is eleased.

20 Potential Fo Multiple Chages The Electic Potential V in in the vicinity of of a numbe of of chages is is equal to to the algebaic sum of of the potentials due to to each chage. Q A Q 3 - Q 2 V A kq kq kq kq V 3 Potential is is + o o based on sign of of the chages Q.

21 Example 5: Two chages Q 1 = +3 nc and Q 2 = -55 nc ae sepaated by 8 cm.. Calculate the electic potential at point A. kq 1 kq V A kq kq x 10 Nm 2 ( 3 x 10 C) C (0.06 m) x 10 Nm 2 ( 5 x 10 C) C (0.02 m) V A = 450 V 2250 V; 450 V 2250 V V A = V B Q 1 + A - 2 cm +3 nc 6 cm 2 cm Q 2 = -5 nc

22 Example 5 (Cont.): Calculate the electic potential at point B fo same chages. kq 1 1 kq 2 2 V B kq kq x 10 Nm 2 ( 3 x 10 C) C (0.02 m) x 10 Nm 2 ( 5 x 10 C) C (0.10 m) V B = 1350 V 450 V; 1350 V 450 V V B = +900 V B Q 1 + A - 2 cm +3 nc 6 cm 2 cm Q 2 = -5 nc

23 Example 5 (Cont.): Discuss meaning of the potentials just found fo points A and B. Conside Point A: V A = V Fo evey coulomb of of positive chage placed at at point A, the potential enegy will be 1800 J. J. (Negative P.E.) The field holds on to to this positive chage. An extenal foce must do J of of wok to to emove each coulomb of of + chage to to infinity. B Q 1 + A - 2 cm +3 nc 6 cm 2 cm Q 2 = -5 nc

24 Example 5 (Cont.): Discuss meaning of the potentials just found fo points A and B. Conside Point B: V B = +900 V Fo evey coulomb of of positive chage placed at at point B, the potential enegy will be +900 J. J. (Positive P.E.) Fo evey coulomb of of positive chage, the field E will do 900 J of of positive wok in in emoving it it to to infinity. B Q 1 A + 2 cm +3 nc 6 cm 2 cm - Q 2 = -5 nc

25 Potential Diffeence The potential diffeence between two points A and B is is the wok pe unit positive chage done by electic foces in in moving a small test chage fom the point of of highe potential to to the point of of lowe potential. Potential Diffeence: V AB AB = V A -V B Wok AB AB = q(v A V B ) Wok BY E-field The positive and negative signs of of the chages may be used mathematically to to give appopiate signs.

26 Example 6: What is the potential diffeence between points A and B.. What wok is done by the E-field E if a +2 C chage is moved fom A to B? B 2 cm V A = V V B = +900 V Q nc V AB = V A V B = V 900 V V AB AB = V Note point B is at highe potential. Wok AB = q(v A V B ) = (2 x 10-6 C )(-2700 V) A Q 2-6 cm 2 cm -5 nc Wok = mj E-field does negative wok. Thus, an extenal foce was equied to move the chage.

27 Example 6 (Cont.): Now suppose the +2 C chage is moved fom back fom B to A? B 2 cm V A = V V B = +900 V Q nc V BA = V B V A = 900 V (-1800 V) V BA BA = V This path is fom high to low potential. Wok BA = q(v B V A ) = (2 x 10-6 C )(+2700 V) A Q 2-6 cm 2 cm -5 nc Wok = mj E-field does positive wok. The wok is done BY the E-field this time!

28 Paallel Plates Conside Two paallel plates of equal and opposite chage, a distance d apat. Constant E field: F = qe Wok = Fd = (qe)d( Also, Wok = q(v A V B ) So that: qv AB = qed qv AB and V A q F = qe V B V AB AB = Ed E The potential diffeence between two oppositely chaged paallel plates is is the poduct of of E and d. d.

29 Example 7: The potential diffeence between two paallel plates is 800 V. If thei sepaation is 3 mm,, what is the field E? V A q F = qe V B E V V Ed; E d 80 V E 26,700 V/m m The E-field expessed in in volts pe mete (V/m) is is known as as the potential gadient and is is equivalent to to the N/C. The volt pe mete is is the bette unit fo cuent electicity, the N/C is is bette electostatics.

30 Summay of Fomulas Electic Potential Enegy and Potential U kqq ; V U q Electic Potential Nea Multiple chages: V kq Wok AB AB = q(v A V B ) Wok BY E-field Oppositely Chaged Paallel Plates: V V Ed; E d

31 CONCLUSION: Chapte 25 Electic Potential

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is