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العرض التّقديمي يتمّ تحميله. الرّجاء الانتظار

25-1 Potential Differences and Electric Potential

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1 25-1 Potential Differences and Electric Potential
25-1 Potential Differences in a Uniform Electric Field 25-3 Electric Potential and Potential Energy due to Point Charges Fig 25-CO Processes occurring during thunderstorms cause large differences in electric potential between a thundercloud and the ground. The result of this potential difference is an electrical discharge that we call lightning, such as this display over Tucson, Arizona. (© Keith Kent/Photo Researchers, Inc.) Fig 25-CO, p.762

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 When a test charge q0 is placed in an electric field E created by some other charged object, the electric force acting on the test charge is q0E. The force q 0E is conservative because the individual forces described by Coulomb’s law are conservative. F q Fe When the test charge is moved in the field by some external agent, the work done by the field on the charge is……….

4 When the test charge is moved in the field by some external agent, the work done by the field on the charge is equal to the negative of the work done by the external agent causing the Displacement. F q Fe

5 Because the force q0E is conservative, this line integral does not
depend on the path taken from A to B. Figure 25.1 (Quick Quiz 25.1) Two points in an electric field. There is a potential difference between the two points. Fig 25-1, p.765

6 The potential energy per unit charge U/q0 is independent of the value of q0 and has a unique value at every point in an electric field. This quantity U/q0 is called the electric potential (or simply the potential) V. Thus, the electric potential at any point in an electric field is

7 The fact that potential energy is a scalar quantity means that electric potential also is a scalar quantity. Electric potential 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, we are referring to the charge–field system.

8 Definition: The potential difference ΔV between points A and B equals the work per unit charge that an external agent must perform to move a test charge from A to B without changing the kinetic energy of the test charge. Just as with potential energy, only differences in electric potential are meaningful. Electric potential V at an arbitrary point in an electric field equals the work required per unit charge to bring a positive test charge from infinity to that point.

9 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 an electron (or proton) gains or loses by moving through a potential difference of 1 V. Because 1 V 1 J/C and because the fundamental charge is 1.6x10-19 C approximately the electron volt is related to the joule as follows: 1 eV = 1.6 x10-19 C x 1 V = 1.60 x J

10 3. (a) Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same potential difference.

11 25-2 فرق الجهد الكهربي في المجال المتجانس (المنتظم)
مجال الجاذبية الأرضية طاقة الوضع المجال الكهربي طاقة الوضع الكهربية Figure 25.2 (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. (b) When an object of mass m moves downward in the direction of the gravitational field g, the object–field system loses gravitational potential energy. Fig 25-2, p.765

12 Figure 25.2 (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. (b) When an object of mass m moves downward in the direction of the gravitational field g, the object–field system loses gravitational potential energy. Fig 25-2, p.765

13 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. Figure 25.2 (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. Fig 25-2a, p.765

14 (b) When an object of mass m moves downward in the direction of the gravitational field g, the object–field system loses gravitational potential energy. Figure 25.2 (b) When an object of mass m moves downward in the direction of the gravitational field g, the object–field system loses gravitational potential energy. Fig 25-2b, p.765

15 عندما ينتقل جسم كتلته ( ) من النقطة ا على النقطة ب داخل
عندما ينتقل جسم كتلته ( ) من النقطة ا على النقطة ب داخل مجال الجاذبية الأرضية فأن منظومة الجسم-المجال يفقد طاقة وضع أي ان التغير في طاقة الوضع يكون سالبا. Figure 25.2 (b) When an object of mass m moves downward in the direction of the gravitational field g, the object–field system loses gravitational potential energy. Fig 25-2b, p.765

16 عندما يتجه المجال إلى أسفل، فأن الانتقال لشحنة الاختبار-
شحنة وهمية أو صغيرة جدا موجبة- من النقطة ا على النقطة ب فأن منظومة الشحنة-المجال يفقد طاقة وضع أي ان التغير في طاقة الوضع يكون سالبا ويكون فرق الجهد الكهربي كذلك سالبا أي أن المطلق للنقطة ا يكون أكبر من الجهد المطلق للنقطة ب. Figure 25.2 (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. Fig 25-2a, p.765

17 التغير في طاقة الوضع يكون سالبا للشحنة الموجبة، أي ان طاقة الوضع تقل، ويكون التغير في طاقة الوضع
موجبا للشحنة السالبة، أي ان طاقة الوضع تزداد عندما تنتقل الشحنة بين نقطتين في اتجاه المجال الكهربي كما هو موضح بالشكل السابق. الشحنة الموجبة اذا تحركت داخل المجال بحرية فإنها تتحرك في اتجاه المجال وتزداد سرعتها وطاقتها الحركية ومن ثم فان المجال يفقد كمية مساوية من طاقة الوضع الكهربية.

18 أي ان الانتقال بين نقطتين حيث المسار
عندما تنتقل الشحنة داخل المجال وتكون الإزاحة لا توازي المجال الكهربي – أي انها تصنع زاوية مع خطوط المجال VB – VA = VC - VA مجال كهربي منتظم أي ان الانتقال بين نقطتين حيث المسار يكون عموديا على خطوط المجال، θ=900 فان فرق الجهد يساوي صفر – متساويا الجهد ولا يلزم بذل أي شغل لنقل الشحنة. ويكون النقطتين على سطح تساوي الجهد وكذلك طاقة الوضع الكهربية. Figure 25.3 A uniform electric field directed along the positive x axis. Point B is at a lower electric potential than point A. Points B and C are at the same electric potential. AC = s cos θ Fig 25-3, p.766

19 أسطح تساوي الجهد Figure 25.4 (Quick Quiz 25.3) Four equipotential surfaces. Fig 25-4, p.766

20 أسطح تساوي الجهد

21 أسطح تساوي الجهد

22 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= cm, and we assume the electric field between the plates to be uniform.؟ Figure 25.5 (Example 25.1) A 12-V battery connected to two parallel plates. The electric field between the plates has a magnitude given by the potential difference V divided by the plate separation d. Fig 25-5, p.767

23 A proton is released from rest in a uniform electric field that has a magnitude of 8.0 x104 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. Figure 25.6 (Example 25.2) A proton accelerates from A to B in the direction of the electric field. H.W.: Use the concept of conservation of energy to find the speed of the proton at point B. Fig 25-6, p.767

24 أي علاقة بشكل المسار الواصل بين النقطتين.
Figure 25.7 The potential difference between points A and B due to a point charge q depends only on the initial and final radial coordinates rA and rB. The two dashed circles represent intersections of spherical equipotential surfaces with the page. من العلاقة الأخيرة، فان فرق الجهد بين النقطة ا & النقطة ب يعتمد على بعد كلا النقطتين من الشحنة وليس له أي علاقة بشكل المسار الواصل بين النقطتين. Fig 25-7, p.768

25 الجهد المطلق؛ الجهد عند النقطة ب، حيث rB=r ، rA = α &
يكون الجهد المطلق موجبا حول الشحنة الموجبة وتكون سالبة حول الشحنة السالبة & أما اذا كان هناك مجموعة من الشحنات فان الجهد المطلق يكون موجبا أو سالبا حسب محصلة الشحنات – موجبا أو سالبة. q2 q3 q4 P q1 q5 جمع قياسي للشحنة

26 Figure 25.8 The electric potential in the plane around a single positive charge is plotted on the vertical axis. (The electric potential function for a negative charge would look like a hole instead of a hill.) The red line shows the 1/r nature of the electric potential, as given by Equation Fig 25-8, p.769

27 Figure 25.9 The electric potential in the plane containing a dipole.
Fig 25-9, p.769

28 الجهد الكهربي المطلق عند النقطة p تكون ناتجة عن
Active Figure (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 . Fig 25-10, p.770

29 في حالة وجود أكثر من شحنة كهربي فان طاقة الوضع الكهربية لهذه المنظومة تكون؛
Figure Three point charges are fixed at the positions shown. The potential energy of this system of charges is given by Equation Fig 25-11, p.770

30 Figure (Example 25.3) (a) The electric potential at P due to the two charges q1 and q2 is the algebraic sum of the potentials due to the individual charges. (b) A third charge q3 = 3.00 C is brought from infinity to a position near the other charges. Fig 25-12, p.771

31 Figure (Example 25.3) (a) The electric potential at P due to the two charges q1 and q2 is the algebraic sum of the potentials due to the individual charges. Fig 25-12a, p.771

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