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Chapter 25 :Electric potential 25-1 Potential difference and electric Potential

Chapter 25 :Electric potential 25-1 Potential difference and electric Potential 25-2 Potential Difference and electric field 25-3 Electric Potential and Potential energy due to point charges. 25-1 Potential difference and electric Potential.

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Chapter 25 :Electric potential 25-1 Potential difference and electric Potential

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  1. Chapter 25 :Electric potential 25-1 Potential difference and electric Potential 25-2 Potential Difference and electric field 25-3 Electric Potential and Potential energy due to point charges Norah Ali Al-moneef king saud university

  2. 25-1 Potential difference and electric Potential Norah Ali Al-moneef king saud university

  3. Work and Potential Energy Work Energy Theorem a b Norah Ali Al-moneef king saud university

  4. a b Electric Potential Difference Definition: Norah Ali Al-moneef king saud university

  5. Conventions for the potential “zero point” “Potential” 0 0 If Va=0 Norah Ali Al-moneef king saud university

  6. 25-2 Potential Difference and electric field Change in electric potential energy is negative of work done by electric force: Norah Ali Al-moneef king saud university

  7. Norah Ali Al-moneef king saud university

  8. Unit of Electric Potential Norah Ali Al-moneef king saud university

  9. Example If a 9 V battery has a charge of 46 C how much chemical energy does the battery have? E = V x Q = 9 V x 46C = 414 Joules Norah Ali Al-moneef king saud university

  10. Example A pair of oppositely charged, parallel plates are separated by 5.33 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field strength between the plates? (b) What is the magnitude of the force on an electron between the plates? Norah Ali Al-moneef king saud university

  11. Example Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V Norah Ali Al-moneef king saud university

  12. Norah Ali Al-moneef king saud university

  13. Superposition of potentials +Q1 +Q2 0 +Q3 Norah Ali Al-moneef king saud university

  14. Norah Ali Al-moneef king saud university

  15. 11/7/2019 Norah Ali Al-moneef king saud university Norah Ali Al-moneef king saud university 16

  16. Norah Ali Al-moneef king saud university

  17. Example (25.2) 11/7/2019 Norah Ali Al-moneef king saud university Norah Ali Al-moneef king saud university 18

  18. 11/7/2019 Norah Ali Al-moneef king saud university Norah Ali Al-moneef king saud university 19

  19. Example An electric dipole consists of two charges q1 = +12nC and q2 = -12nC, placed 10 cm apart as shown in the figure. Compute the potential at points a,b, and c. Norah Ali Al-moneef king saud university

  20. Example The Total Electric Potential At locations A and B, find the total electric potential.

  21. (a) If two point charges are separated by a distance r12, the potential energy of the pair of charges is given by keq1q2/r 12 . (b) If charge q1 is removed, a potential keq2/r 12 exists at point P due to charge q 2 . Norah Ali Al-moneef king saud university

  22. +Q2 +Q2 +Q1 +Q3 Potential energy due to multiple point charges +Q1 Norah Ali Al-moneef king saud university

  23. A · +2 nC +Q +6 mC Example 1. What is the potential energy if a +2 nC charge moves from ¥ to point A, 8 cm away from a +6 mC charge? The P.E. will be positive at point A, because the field can do + work if q is released. 8 cm Potential Energy: U = 1.35 mJ Positive potential energy Norah Ali Al-moneef king saud university

  24. B · A · 12 cm 8 cm C · Questions: 4 cm +Q If +2 nC moves from A to B, does field E do + or – work? Does P.E. increase or decrease? +6 mC Moving positive q +2 nC Signs for Potential Energy Consider Points A, B, and C. For +2 nC at A: U = +1.35 mJ The field E does positive work, the P.E. decreases. If +2 nC moves from A to C (closer to +Q), the field E does negativework and P.E. increases. Norah Ali Al-moneef king saud university

  25. B · A · 12 cm 8 cm +Q +6 mC Example. What is the change in potential energy if a +2 nC charge moves from Ato B? Potential Energy: From Ex-1: UA = + 1.35 mJ DU = UB – UA = 0.9 mJ – 1.35 mJ DU = -0.450 mJ Note that P.E. has decreased as work is done by E. Norah Ali Al-moneef king saud university

  26. B · A · 12 cm 8 cm +Q +6 mC Example What is the change in potential energy if a -2 nC charge moves from A to B? Potential Energy: From Ex-1: UA = -1.35 mJ (Negative due to – charge) DU = +0.450 mJ UB – UA = -0.9 mJ – (-1.35 mJ) A – charge moved away from a + charge gains P.E. Norah Ali Al-moneef king saud university

  27. - - P - . - 6 cm r Q - - - - Q = -5 nC Example :Find the potential at a distance of 6 cm from a –5 nC charge. q = –4 mC Negative V at Point P : VP = -750 V What would be the P.E. of a –4 mC charge placed at this point P? U = 3.00 mJ U = qV = (-4 x 10-6mC)(-750 V); Since P.E. is positive, E will do + work if q is released. Norah Ali Al-moneef king saud university

  28. B · 2 cm Q1 +3 nC 6 cm - A · 2 cm + Q2 = -5 nC Example : Two charges Q1= +3 nC and Q2 = -5 nC are separated by 8 cm. Calculate the electric potential at point A. VA = -1800 V VA = 450 V – 2250 V; Norah Ali Al-moneef king saud university

  29. B · 2 cm Q1 +3 nC 6 cm - A · 2 cm + Q2 = -5 nC Example Calculate the electric potential at point B for same charges. VB = +900 V VB = 1350 V – 450 V; Norah Ali Al-moneef king saud university

  30. · B 2 cm Q1 +3 nC + 6 cm A · 2 cm - -5 nC Q2 Example : What is the potential difference between points A and B. What work is done by the E-field if a +2 mC charge is moved from A to B? VA = -1800 V VB = +900 V VAB= VA – VB = -1800 V – 900 V Note point B is athigher potential. VAB = -2700 V WorkAB = q(VA – VB) = (2 x 10-6 C )(-2700 V) Work = -5.40 mJ E-field does negative work. Thus, an external force was required to move the charge. Norah Ali Al-moneef king saud university

  31. · B 2 cm Q1 +3 nC + 6 cm A · 2 cm - -5 nC Q2 Example 6 (Cont.): Now suppose the +2 mC charge is moved from back from B to A? VA = -1800 V VB = +900 V VBA= VB – VA = 900 V – (-1800 V) This path is from high to low potential. VBA = +2700 V WorkBA = q(VB – VA) = (2 x 10-6 C )(+2700 V) Work = +5.40 mJ E-field does positive work. The work is done BY the E-field this time ! Norah Ali Al-moneef king saud university

  32. Example An electron is accelerated in a TV tube through a potential difference of 5000 V. a) What is the change in PE of the electron? V = DPE/q DPE = qV = (-1.60 X 10-19 C)(+5000 V)= -8.0 X 10-16 J What is the final speed of the electron (m = 9.1 X 10-31 kg) DPE + DKE = 0 (Law of conservation of energy) DPE = -DKE DPE = - ½ mv2 v2 = (-2)(DPE) = (-2)(-8.0 X 10-16 J) m 9.1 X 10-31 kg v = 4.2 X 107 m/s Norah Ali Al-moneef king saud university

  33. Summary • Electric potential energy: • Electric potential difference: work done to move charge from one point to another • Relationship between potential difference and field: • Equipotential: line or surface along which potential is the same • Electric potential of a point charge: Norah Ali Al-moneef king saud university

  34. 1: 2: Norah Ali Al-moneef king saud university

  35. 3: 4: Norah Ali Al-moneef king saud university

  36. 5: • The electrons in a particle beam each have a kinetic energy of 1.60 x 10-17 J. What are the magnitude and direction of the electric field that stops these electrons in a distance of 10.0 cm? • An electron and a proton are each placed at rest in an electric field of 520 N/C. Calculate the speed of each particle 48.0 ns after being released. 6: Norah Ali Al-moneef king saud university

  37. q1 q2 d d P d d q4 q3 q1 = +12 n C, q2= -24 n C q3 = +31 n C, q4= +17 n C 7: What is the potential at point P, located at the center of the square of point charges. Assume that d = 1.3m and the charges are Norah Ali Al-moneef king saud university

  38. 1- The electric field has a magnitude of 3.0 N/m at a distance of 60 cm from a point charge. What is the charge? (a) 1.4 nC (b) 120 pC (c) 36 mC (d) 12 C (e) 3.0 nC Norah Ali Al-moneef king saud university

  39. Electric charge always occurs in multiples ofe 19 e 1.60 10 C = × Q = Ne (N =1、2、3…) 1- A conducting sphere has a net charge of −4.8 × 10−17 C. What is the approximate number of excess electrons on the sphere? (a) 100 (b) 200 (c) 300 (d) 400 (e) 500 N= (-4.8x10-17 C/-1.6x10-19 C=300 electrons) • 2- Two point charges, 8x10-9 C and -2x10-9 C are separated by 4 m. The electric field magnitude (in units of V/m) midway between them is: • 9x109 B) 13,500 C) 135,000 D) 36x10-9 E) 22.5 Norah Ali Al-moneef king saud university

  40. Norah Ali Al-moneef king saud university

  41. 3 - If 10000 electrons are removed from a neutral ball, its charge is; • +1.6×10-15 C (b) +1.6×10-23 C • (c) -1.6×10-15 C (d) -1.6×10-23 C Q = Ne =10000 x -1.6×10-19 Q = -1.6×10-15 C 4 - A charge of 10-6 C is in a field of 9000 N/C, directed upwards. The magnitude and direction of the force it experiences are; (a) 9×10-3 N, downwards (b) 3×10-3 N, downwards (c) 9×10-3 N, upwards (d) 3×10-3 N, upwards F= q E = 9000 x 10-6 F = 9 x 10 -3 N Norah Ali Al-moneef king saud university

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