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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 Slide 1 Fig 25-CO, p.762 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. Slide 2 When a test charge q0 is placed in an electric field E created by some other charged object, the electric force Fe acting on the test charge is equal to q0E. When the test charge is moved in the electric field by some external agent, the work done (W) by the electric field on the q charge is equal to the negative of the work done by the external agent causing the displacement ds. Slide 3 Work (W ) Fe .ds q0 E.ds 1. Work done (W) = Potential energy (U) U Fe .ds q0 E.ds 2. Change in potential energy (U) between B and A is given B U U B U A qo E .ds A Potential energy (U) is a scalar quantity Slide 4 3. The electric potential = potential (V). The electric potential at any point in an electric field is 4. The potential difference U V q0 V VB VA 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 q0 : U V E.ds q0 A B 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 referring to the charge–field system Slide 5 energy (U), we are 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): U Work V q0 ch arg e Volt x electron charge = electron volt ( eV) 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 Slide 6 25.2 Potential Deference in a uniform Electric Filed 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 V VB VA E . ds A B E ds cos A B E ds cos 0 V Slide 7 A Ed U qo V qo E d Fig 25-2a, p.765 Slide 8 Equipotential Surface uniform electric field Find the electric potential difference VB –VA through the path AB and ACB AC = d = s cos θ Slide 9 AC = d = s cos θ Slide 10 Slide 11 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 Slide 12 Fig 25-4, p.766 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.؟ Slide 13 Fig 25-5, p.767 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. H.W.: Use the concept of conservation of energy to find the speed of the proton at point B. Slide 14 Fig 25-6, p.767 B V B V A E .ds A q q E .ds k e 2 r .ds k e 2 ds cos r r q k e 2 dr r B Slide 15 rB V B V A dr E dr k e q 2 r A rA V B V A 1 1 k eq ( ) rB rA Fig 25-7, p.768 Electric potential created by a point charge If rB = r , rA = α , 1/ rA= 0 , The electric potential created by a point charge at any distance r from the charge is q V ke r Electric potential due to several point charges For a group of point charges, we can write the total electric potential at P in the form P q1 Slide 16 q2 q 3 q4 q5 qi V ke ri Electric potential energy due to two charges U V q1 q1 q2 U ke r12 Slide 17 The total potential energy of the system of three charges is q1 q2 q1 q3 q2 q3 U ke ( ) r12 r13 r23 U ke Slide 18 qij rij Fig 25-11, p.770 Slide 19 Fig 25-12, p.771 Slide 20 Fig 25-12a, p.771 Slide 21 Slide 22 Slide 23 If the electric field E is in the x direction it will has only one component Ex, then Therefore, Slide 24 Or E often is written as: Slide 25 مثال 1 يعطي الجهد الكهربائي في منطقة ما بالمعادلة التالية: اوجد المجال الكهربائي عند النقطة التي إحداثياتها Slide 26 Slide 27 Homework (2) Slide 28 Slide 29 Slide 30 Slide 31 Slide 32 q1 q2 q1 q3 q2 q3 U ke ( ) r12 r13 r23 Slide 33 U ke qij rij The potential gradients is : Slide 34