Chapter 23

Electric Fields

Intro

• The electromagnetic force between particles is one of the four fundamental forces of nature.

• We will begin by discussing electric charges and the forces associated.

• We will then look at the electric field produced by a distribution of charges.

• Finally we will examine the motion of a charged particle in an electric field.

23.1 Properties of Electric Charges

• An object is Electrically Charged if it has an imbalance between the two fundamental types of charge.

• Positive and Negative Charges, names given by Benjamin Franklin are how we identify the charge of a proton and electron respectively.

• The behavior of charged objects is commonly observed.

23.1

• Opposite Charges exhibit attractive forces.

23.1

• Similar Charges exhibit repellant forces.

23.1

• Electric Charge is always conserved. – When one object is rubbed against another,

charge is not created.– The charged state occurs due to a transfer of

charge from one object to another. – Whatever one object gains, the other object loses

(for isolated systems). – Glass/Silk and Rubber/Fur

23.1

23.1

• Charge is quantized– The fundamental “charge packet” is e.– All charges represent an integer multiple of e.

– The charges of a proton and electron are +e and -e respectively.

Quick Quizzes p 709

Neq

23.2 Charging by Induction

• Material Classification– Conductor- material that has free electrons, not

bound to atoms, able to move freely through the material• Typically metals- copper, silver, aluminum• Metallic bonding leaves free electrons

– Insulator- material in which all electrons are bound to atoms, and cannot freely move. • Glass, rubber, wood• Charges remain in a given area, are not free to move

23.2

– Semiconductors- electrical properties somewhere between conductors and insulators.• Silicon, Germanium• The properties can be modified by the addition of

controlled amounts of certain atoms to pure semiconductors.• The process is called “doping”

23.2

• Stripping electrons from one material to another is not the only way to produce a charge.

• Induction- one process for charging a conductor. • Consider a neutral conducting sphere.

23.2

• A charged rod is brought near the sphere.

• The sphere is attached to ground. The excesselectrons flow to ground.

23.2

• Ground- any electron reservoir (a source that can give/receive electrons freely without significant change to its overall electrical characteristics)

• Ex: Earth, Car Frame

23.2

• The ground wire is removed

• The charged rod is removed leaving the conducting sphere with more positive charge than negative.

23.2

• Charges can be induced in insulators even with the lack of free electrons. • The molecules can be realigned in the presence of an electric charge, producing a layer of charge on the surface of the insulator.

23.2

• Quick Quiz p. 711

23.3 Coulomb’s Law

• Charles Coulomb was able to measure the electric force between charged objects using his torsion balance (very similar in idea to the Cavendish Experiment)

23.3

• He was able to verify the following conclusions about the electric force.– Follows the inverse square law.– Proportional the product of the charges q1 and q2

– The force is attractive if charges are opposite sign, repulsive if they have the same sign.

– The electric force is conservative.

23.3

• Coulomb’s Law determines the electric force between two point charges.

• Where ke is the Coulomb constant, q1 and q2 are the particle charges, r is the distance between them

221

rqqkF ee

23.3

• The SI unit for charge, q, is the Coulomb (C)– 1 C ≈ The charge of 6.24 x 1018 Electrons (e)– 1 e = 1.602 x 10-19 C

• The coulomb constant

• εo is called the Vacuum Permittivityo

e CmNxk41/109875.8 229

2212 /108542.8 mNCxo

23.3

• Remember, Force is a vector quantity.• The force of q1 on q2 is equal and opposite of

q2 on q1

• Quick Quizzes p 712-13• Examples 23.1-23.4

23.4 Electric Field

• The electric force is a field force– The force can act through empty space, (like

gravity) no contact is required.• An electric Field exists in the region

surrounding a charged object.– This is the source charge.

• When a second charge, is brought into the field, an electric force acts on it– This is the test charge.

23.4

• The electric field is defined as the Electric Force on the test charge per unit of charge. (N/C)– Just like gravitational field (the gravitational force

per unit of mass N/kg or m/s2)

o

e

qFE

mgFg

23.4

• The direction of the Electric Field vector is determined by which direction the force would act on a Positive test charge. – Points away from a positive source charge.– Points towards a negative source charge.

• The magnitude of the E-Field around any point source charge can be found by.

o

o

o

e

qrqqk

qFE

2 2r

kqE

23.4

• Example 23.5, 23.6

23.5 Electric field from a Continuous Charge Distribution

• How to we determine the electric field caused by an object other than a point charge.

• We will look at symmetrical objects on which the charge is evenly distributed.

• We will “add up” the E-field created by each “tiny piece” of the charged object.

• We will integrate over the entire charge distribution.

23.5

• This is a vector operation and direction will need to be accounted for appropriately.

• We will be looking at the charges evenly distributed on a line, on a surface, or throughout a volume.

• Charge density will become a convenient factor.

rE ˆ2rdqke

23.5

• Charge Density– Volumetric- charge per unit volume (C/m3)

– Surface- charge per unit area (C/m2)

– Linear- charge per unit length (C/m)

VQ

AQ

Q

23.5

• When looking at the amount of charge on a small piece of the object for integration…– Volume dq = ρdV– Surface dq = σdA– Line dq = λdl

23.5

• See Board Diagrams• Examples 23.7-23.9

23.6 Electric Field Lines

• To Show the electric field pictorially, electric field line diagrams can be drawn.

• The Electric Field vector E is tangent to the field line at any point.

• The number of field lines through a surface per unit area is proportional to the magnitude of the electric field in that region.

23.6

• On a positive point charge-– The electric field lines radiateoutward in all directions– In 3D, the distribution is spherical.– A positive test charge would be repelled from the sourcecharge.

23.6

• On a negative point charge-– The field lines radiate inwardin all directions.– A positive test charge wouldbe attracted to the sourcecharge.

23.6

• For an electric Dipole (equal/opposite charges)– The number of field lines leaving the positive charge equals the number of field lines terminating on the negative charge.

23.6

• Equal and Like Charges– The same number of charges leave both particles.– At a great distance the field approximates to that of a single 2q charge.

23.6

• Opposite/Unequal Charges– The number of lines leaving/terminating each charge is proportional to their relative charges (in this case, 2 to 1)– At a great distance the E field would approximate to that of a single charge q.

23.6

• Drawing Electric Field Lines– The lines must begin on a positive charge and

terminate on a negative charge. • With a charge imbalance, some lines will begin/end

infinitely far away.– The number of lines beginning/terminating is

proportional to the relative charges.– The fields lines can not cross.

• Quick Quizzes p 725

23.7 The Motion of Charged Particles in an Electric Field

• A charged particle in an electric field experiences an Electric force.

• If this is the only force acting, Fe is the net force.

• The charged particle will accelerate according to Newton’s 2nd Law

aEF mqe

23.7

• If E is uniform, then a is a constant value. – If the charge is positive, the acceleration vector

points with the E-field.– If the charge is negative, the acceleration vector

points against the E-field.• Since acceleration is constant, kinematics

equations can be use. • Example 23.10 p 726

23.7

• Charged Projectiles-– The charged particle can follow a 2D projectile

path if it has velocity perpendicular to the E-field.

– Example23.11 pg 727

23.7

• The Cathode Ray Tube (CRT)– Used for display of electronic information• Oscilloscopes, Radar systems, TV/Computer Monitors