25 1 Potential Differences and Electric Potential 25

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25 -1 Potential Differences and Electric Potential 25 -2 Potential Differences in a Uniform

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

Ø When a test charge q 0 is placed in an electric field E

Ø When a test charge q 0 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 q 0 E. ØWhen 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. Slide 7

1. Work done (W) = Potential energy (U) 2. Change in potential energy (

1. Work done (W) = Potential energy (U) 2. Change in potential energy ( U) between B and A is given Potential energy (U) is a scalar quantity Slide 8

3. The electric potential = potential (V). The electric potential at any point in

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 Slide 9

Because electric potential is a measure of potential energy per unit charge, the SI

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): Volt x electron charge = electron volt ( e. V) Electron volt (e. V), which is defined as the energy gains or loses of an electron (or proton) by moving through a potential difference of 1 V. 1 e. V = 1. 6 x 10 -19 C x 1 V = 1. 60 x 10 -19 J Slide 10

25. 2 Potential Deference in a uniform Electric Filed a) When the electric field

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. Slide 11 Fig 25 -2 a, p. 765

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Equipotential Surface uniform electric field Find the electric potential difference VB –VA through the

Equipotential Surface uniform electric field Find the electric potential difference VB –VA through the path AB and ACB AC = d = s cos θ Slide 13

AC = d = s cos θ Slide 14

AC = d = s cos θ Slide 14

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An equipotential surface is any surface consisting of a continuous distribution of points having

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 17 Fig 25 -4, p. 766

A battery produces a specified potential difference between conductors attached to the battery terminals.

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 18 Fig 25 -5, p. 767

A proton is released from rest in a uniform electric field that has a

A proton is released from rest in a uniform electric field that has a magnitude of 8. 0 x 104 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 19 Fig 25 -6, p. 767

Slide 20 Fig 25 -7, p. 768

Slide 20 Fig 25 -7, p. 768

v. Electric potential created by a point charge If r. B = r ,

v. Electric potential created by a point charge 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 v. 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 q 1 Slide 21 q 2 q 3 q 4 q 5

v. Electric potential energy due to two charges Slide 22

v. Electric potential energy due to two charges Slide 22

v. The total potential energy of the system of three charges is Slide 23

v. The total potential energy of the system of three charges is Slide 23 Fig 25 -11, p. 770

Slide 24 Fig 25 -12, p. 771

Slide 24 Fig 25 -12, p. 771

Slide 25 Fig 25 -12 a, p. 771

Slide 25 Fig 25 -12 a, p. 771

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If the electric field E is in the x direction it will has only

If the electric field E is in the x direction it will has only one component Ex, then Therefore, Slide 29

Or E often is written as: Slide 30

Or E often is written as: Slide 30

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Homework (2) Slide 33

Homework (2) Slide 33

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The potential gradients is : Slide 39

The potential gradients is : Slide 39