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Chapter 20

Electric Potential and Electric Potential Energy

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Outline

Electrical potential energy, U Electrical potential, V Connection between electric field E

and electric potential V Energy conservation Electrical potential of point charges

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Electrical Potential Energy, U

Definition for U, the change in electrical potential energy of a charge: U = Uf - Ui = -W The work done by a

conservative force (e.g., an electric force and force of gravity) is equal to the negative of the change in potential energy.

SI units: Joules (J)

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Electrical Potential, V Definition for V, the change in electric

potential: V = Vf – Vi = U/q0 = (-W)/q0 V is the change in electric potential energy

per charge. SI units: Joules/Coulomb (J/C) = Volt (V)

Relationship between U and V: U = q0 V Both are scalar quantities.

Another commonly used unit of energy is the electron volt (eV): 1 eV = (1.60x10-19 C)(1 V) = 1.60x10-19 J

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Exercise 20-1

Find the change in electric potential energy, U, as a charge of (a) 2.20 x 10-6

C or (b) -1.10 x 10-6 C moves from a point A to a point B, given that the change in electric potential between these points is V = VB – VA = 24.0 V.

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Connection between Electric Field and Electric Potential

Connection between the electric field and the electric potential:

E = -V/s V = -Es

The electric field depends on the rate of change of the electric potential with position.

The electric potential decreases as one moves in the direction of the electric field.

SI units for E: 1 N/C = 1 V/m

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Example 20-1: Plates at Different Potentials

A uniform electric field is established by connecting the plates of a parallel-plate capacitor to a 12-V battery.

(a) If d = 0.75 cm, what is the magnitude of the electric field in the capacitor?

(b) A charge of +6.24x10-6 C moves from the positive plate to the negative plate. Find the change in electric potential energy.

(In electrical systems, we shall assume that gravity can be ignored, unless specifically instructed otherwise.)

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Energy Conservation

Energy conservation: For a charged object in an electric field, its total energy must be conserved. KA + UA = KB + UB, or (1/2)mvA

2 + UA = (1/2)mvB

2 + UB

Example 20-2: What is (a) the mass of the charge and (b) its final kinetic energy?

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Example 20-2: From Plate to Plate

Suppose a charge q = +6.24 x 10-6 C is released from rest at the positive plate and that it reaches the negative plate with a speed of 3.4 m/s.

(a) What is the mass of the charge?

(b) What is its final kinetic energy?

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The Electric Potential of Point Charges

Electric potential V produced by a point charge q at a distance r:

Conventionally, choosing the electric potential to be zero at infinity, V = kq/r

Electric potential energy U for point charges q and q0 separated by a distance r:

U = q0V = kq0q/r Exercise 20-2: Find the electric

potential by a point charge of 6.80x10-7 C at a distance of 2.60 m.

“+” charge

“-” charge

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Homework #2

Chapter 20, P. 717-718, Problems: #2, 4, 19 (Physics, Walker, 4th edition).