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AP PhysicsAP PhysicsToday’s AgendaToday’s Agenda

CHAPTER 16 - ELECTRIC POTENTIAL AND ELECTRIC ENERGY; CAPACITANCE Chp 16 problems 1,5,7,9,13,15,17,19

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OBJECTIVES:After studying the material of this chapter the student should be able to:

1. Write from memory the definitions of electric potential and electric potential difference.

2. Distinguish between electric potential, electric potential energy and electric potential difference.

3. Draw the electric field pattern and equipotential line pattern which exist between charged objects

4. Determine the magnitude of the potential at a point a known distance from a point charge or an arrangement of point charges.

5. State the relationship between electric potential and electric field and determine the potential difference between two points a fixed distance apart in a region where the electric field is uniform.

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OBJECTIVES

6. Determine the kinetic energy in both joules and electron volts of a charged particle which is accelerated through a given potential difference.

7-9 At a later date 7. Explain what is meant by an electric dipole and determine

the magnitude of the electric dipole moment between two point charges.

8. Given the dimensions, distance between the plates and the dielectric constant of the material between the plates, determine the magnitude of the capacitance of a parallel plate capacitor.

9. Given the capacitance, the dielectric constant and either the potential difference or the charge stored on the plates of a parallel plate capacitor, determine the energy and the energy density stored in the capacitor.

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KEY TERMS AND PHRASES

electric potential electric dipole moment electric potential difference debye

electric potential energy capacitor

voltage farad

equipotential lines microfarad

electron volt picofarad

electric dipole energy density

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ELECTRIC POTENTIAL AND POTENTIAL DIFFERENCE

The ELECTRIC POTENTIAL at point a (Va) equals the electric potential energy (PEa) per unit charge (q) placed at that point.

V A= PE A /q

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The ELECTRIC POTENTIAL The ELECTRIC POTENTIAL DIFFERENCE between two DIFFERENCE between two points (V points (V AA) is measured by the ) is measured by the work required to move a unit of work required to move a unit of electric charge from point b to electric charge from point b to point a.point a.

V Vabab = V = Vaa - V - Vbb = W = Wab/ab/qq

The potential difference The potential difference can also be discussed in terms of can also be discussed in terms of the change in potential energy of the change in potential energy of a charge q when it is moved a charge q when it is moved between points a and b.between points a and b.

PE = PEa - PEb= q V., and PE = PEa - PEb= q V., and therefore Vb= therefore Vb= PE/qPE/q

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VOLTAGE

Potential difference is often referred to as VOLTAGE.

Both potential and potential difference are scalar quantities which have dimensions of Joules/Coulomb.

The SI unit of electric potential and potential difference is the VOLT (V), where I V = I J/C.

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Electric Potential and Electric FieldElectric Potential and Electric Field

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Electric Potential and Electric FieldElectric Potential and Electric Field The effects of any charge distribution can be described in terms of

electric field or in terms of electric potential The work done by the electric field to move a positive charge is

W=Vba q The work done by the electric field is also W= Fd where the force

on the positive charge in a uniform electric field is F=qE and d is the distance (parallel to the field lines) between points a and b.

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Electric Potential and Electric FieldElectric Potential and Electric Field W= Fd=q Vba =qEd Vba = Ed (uniform field) E= Vba /d (uniform field) Equivalent units: N/C= Nm/Cm = J/Cm =V/m

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E is the electric field strength in N/C, d is the distance between points a and b in meters and is the angle between the electric field vector and the displacement vector.

a

If the charged particle is in an electric field which is uniform, i.e., constant in magnitude and direction, then the potential difference is related to the electric field as follows Vab = E d Cos

Vab

b

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If the electric field is non-uniform, i.e., varies in magnitude and direction between points a and b, then the electric field strength can only be properly defined over an incremental distance.

a

b

b

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If we consider the x component of the electric field (Ex), then Ex =- V/ x, where V is the change in potential over a very short distance x. The minus sign indicates that E points in the direction of decreasing V.

a

bEx =- V/ x

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EQUIPOTENTIAL LINES EQUIPOTENTIAL LINES are

lines along which each point is at the same potential. On an equipotential surface, each point on the surface is at the same potential. The equipotential line or surface is perpendicular to the direction of the electric field lines at every point. Thus, if the electric field pattern is known, it is possible to determine the pattern of equipotential lines or surfaces,and vice versa.

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In the following diagrams, the dashed lines represent equipotential lines and the solid lines the

electric field lines.

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THE ELECTRON VOLT

The energy gained by a charged particle which is accelerated through a potential difference can be expressed in ELECTRON VOLTS (eV) as well as joules. Higher amounts of energy can be measured in KeV or MeV.

I eV = 1.6 x 10-19 J and I KeV = 103eV and I Mev = 106

eV.

eV is NOT a proper SI Unit. The joules unit should really be used when calculating kinetic energy changes.

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•ELECTRIC POTENTIAL DUE TO A POINT CHARGE

E= kQ/r2 and V= Ed (d can be considered to be the

same as r) therefore V = kQ/r The electric potential due to a point charge q at a

distance r from the charge is given by V = kQ/r= (1/4 0 ) Q/r

Note that the zero of potential is arbitrarily taken to be at infinity ( For a negative charge, the potential at distance r from the charge is less than zero. As r increases, the potential increases toward zero, reaching zero at r)

If more than one point charge is present, the potential at a particular point is equal to the arithmetic sum of the potential due to each charge at the point in question. Sound familiar?

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ELECTRIC DIPOLE

Two equal point charges q, of opposite sign, separated by a distance are called an ELECTRIC DIPOLE.

Since V is equal to the sum of the potentials of the individual charges:

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ELECTRIC DIPOLE

If r >>l the equation can be simplified. (yeah right!) r l cos Since r >> r, it’s contribution to the sum (r + r) can be

neglected in the denominator Therefore

Where is between 0 and 90 degrees,and V is positive. Where is between 90 and 180 degrees,and V is negative Notice that the V depends on r2

As r gets larger, V gets smaller much faster with a dipole……… Why?

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ELECTRIC DIPOLE

The product Ql is the DIPOLE MOMENT (p) and the potential can be written v = k p cos /r2

The SI unit of the dipole moment (p) is the DEBYE, where I debye = 3.33 x 10 C m.

In polar molecules, such as water, the molecule is electrically neutral but there is a separation of charge in the molecule. Such molecules have a net dipole moment.

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CAPACITANCE AND DIELECTRICS

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CAPACITANCE AND DIELECTRICS A CAPACITOR stores electric charge and consists of two

conductors separated by an insulator known as a dielectric. The ability of a capacitor to store electric charge is referred to as CAPACITANCE (C) and is found by the following equation:

C = Q/V Q is the charge stored in coulombs and V is the potential difference

between the conducting surfaces in volts. The SI unit of capacitance is the farad (F), where I farad = I

coulomb/volt (1 F = I C/V). Typical capacitors have values which range from I picofarad (I pF)

to 1 microfarad (1 F) where

I pF = I x 10-12 F and I F =I x 10-6 F

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CAPACITANCE AND DIELECTRICS

The capacitance of a capacitor depends on the physical characteristics of the capacitor as well as the insulating material which separates the conducting surfaces which store the electric charge.

For a parallel plate capacitor, the capacitance is given by C = 0 A/d where 0 is the permittivity of free space = 8.85 x 1O-12 C2/N m2

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CAPACITANCE AND DIELECTRICS

In most capacitors there is an insulating sheet (such as paper or plastic) called a dielectric between the plates.

Dielectrics break down less readily than air and allows plates to be placed closer together (without charge passing across the gap)

For a parallel-plate capacitor C = K 0 A/d

= K 0 where is the permittivity of the material.

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DIELECTRICS

K is the dielectric constant of the insulating material between the plates. The constant isdimensionless and depends on the material. For dry air at 20'C, the constant is 1.0006. E. is the permittivity of free space. A is the surface area of one side of one plate which is opposed by an the equal area of the other plate and d is the distance between the plates. E is the permittivity of the material between the plates.