1. Slide 1Fig 25-CO, p.762 25-1 Potential Differences and Electric Potential 25-2 Potential Differences in a Uniform Electric Field 25-3 Electric Potential and Potential Energy due to Point Charges

2. Slide 2 INTRODUCTION:  Because the electrostatic force given by Coulomb’s law is conservative, electrostatic phenomena can be conveniently described in terms of an electric potential energy. This idea enables us to define a scalar quantity known as electric potential.  Because the electric potential at any point in an electric field is a scalar function, we can use it to describe electrostatic phenomena more simply than if we were to rely only on the concepts of the electric field and electric forces.

3. Slide 3  When a test charge q 0 is placed in an electric field E created by some other charged object, the electric force F e acting on the test charge is equal to q 0 E.  When the test charge is moved in the electric field by some external agent, the work done (W) by the electric field on the charge is equal to the negative of the work done by the external agent causing the displacement ds. q

4. Slide 4 2. Change in potential energy (  U) between B and A is given Potential energy (U) is a scalar quantity 1. Work done (W) = Potential energy (U)

5. Slide 5 3. The electric potential = potential (V). The electric potential at any point in an electric field is 4. The potential difference between any two points A and B in an electric field is defined as the change in potential energy of the system divided by the test charge q 0 : Electric potential (V) is a scalar characteristic of an electric field, independent of the charges that may be placed in the field. However, when we speak of potential energy (  U), we are referring to the charge–field system

6. Slide 6 Because electric potential is a measure of potential energy per unit charge, the SI unit of both electric potential and potential difference is joules per coulomb, which is defined as a volt (V): Electron volt (eV), which is defined as the energy gains or loses of an electron (or proton) by moving through a potential difference of 1 V. 1 eV = 1.6 x10 -19 C x 1 V = 1.60 x 10 -19 J Volt x electron charge = electron volt ( eV)

7. Slide 7Fig 25-2a, p.765 a) When the electric field E is directed downward, point B is at a lower electric potential than point A. When a positive test charge moves from point A to point B, the charge–field system loses electric potential energy. 25.2 Potential Deference in a uniform Electric Filed

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9. Slide 9 Find the electric potential difference V B –V A through the path AB and ACB uniform electric field Equipotential Surface AC = d = s cos θ

10. Slide 10 AC = d = s cos θ

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12. Slide 12Fig 25-4, p.766 An equipotential surface is any surface consisting of a continuous distribution of points having the same electric potential. Equipotential surfaces are perpendicular to electric field lines. Four equi-potential surfaces

13. Slide 13Fig 25-5, p.767 A battery produces a specified potential difference between conductors attached to the battery terminals. A 12-V battery is connected between two parallel plates. The separation between the plates is d= 0.30 cm, and we assume the electric field between the plates to be uniform.؟

14. Slide 14Fig 25-6, p.767 A proton is released from rest in a uniform electric field that has a magnitude of 8.0 x10 4 V/m and is directed along the positive x axis. The proton undergoes a displacement of 0.50 m in the direction of E. (a) Find the change in electric potential between points A and B. (b) Find the change in potential energy of the proton for this displacement. H.W.: Use the concept of conservation of energy to find the speed of the proton at point B.

15. Slide 15Fig 25-7, p.768

16. Slide 16 q1q1 q5q5 q2q2 q3q3 q4q4 P If r B = r, r A = α, 1/ r A = 0, The electric potential created by a point charge at any distance r from the charge is For a group of point charges, we can write the total electric potential at P in the form  Electric potential created by a point charge  Electric potential due to several point charges

17. Slide 17  Electric potential energy due to two charges

18. Slide 18Fig 25-11, p.770  The total potential energy of the system of three charges is

19. Slide 19Fig 25-12, p.771

20. Slide 20Fig 25-12a, p.771

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24. Slide 24 If the electric field E is in the x direction it will has only one component Ex, then Therefore,

25. Slide 25 Or E often is written as:

26. Slide 26 مثال 1 يعطي الجهد الكهربائي في منطقة ما بالمعادلة التالية: اوجد المجال الكهربائي عند النقطة التي إحداثياتها

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28. Slide 28 Homework (2)

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34. Slide 34 The potential gradients is :