Chapter 23 Electric Fields

• Two kinds + and –• Charge is a scalar• Like charges repel and unlike attract• Conductor: charges relatively free to move• Insulator: charges relatively fixed• Charge is conserved in an isolated system – you can

transfer charge, but not create or destroy charge• The MKS unit of charge is 1 Coulomb• Charge is quantized: e = 1.6 x 10-19 Coulombs.

Typically there are around 1013 excess or deficient charges on a body – 1013/1023 or 1 part in 1010

23.1 Properties of Electric Charges

23.2 Induced Charges

CT1: Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces:

A.

B.

C.

D.

E.

F.

G. None of these.

23.3 Coulomb’s Law

F12 = keq1q2/r2 r

ke = 8.99 x 109 Nm2/C2

^

CT2: P23.5 A hydrogen atom is composed of a nucleuscontaining a single proton, about which asingle electron orbits. The electric force between the two particles is 2.3 x 1039 greater than the gravitational force! If we can adjust the distance between the two particles, can we find a separation at which the electric and gravitational forces are equal?

A. Yes, we must move the particles farther apart.

B. Yes, we must move the particles closer together.

C. No, not at any distance

Chapter 23 Electric Fields

Superposition

The effect of several electrical forces acting on a charge due to several other charges is the vector sum of the individual forces from each charge as if the remaining charges weren’t present.

F1 = F21 + F31 + F41 + F51 + F61 + F71 + …..

23.3 Coulomb’s Law

P23.5 (p.666)

P23.8 (p.667)

CT3: P23.8 Which statement is true?A. The charged bead is in stable

equilibrium only if the charge is positive.

B. The charged bead is in stable equilibrium only if the charge is negative.

C. The charged bead is in stable equilibrium if the charge is either positive or negative.

D. The charged bead is in never in stable equilibrium.

I. Definition

Coulomb Force:

Electric Field:

E = lim F/q0 q0 is a positive

q0 0 test charge

Ch23.4 The Electric Field

Chapter 23: Electric Fields

charge1 charge2

charge1 charge2electric

field

II. Calculation of E

A. Point Charge

B. Discrete Distribution of Point Charges

Discrete sum – superposition (P 23.17 and P23.18)

Note: E depends only on the source charge(s)

Ch23.4 The Electric Field

Chapter 23: Electric Fields

CT4: P23.18For very large x

A. The dipole field is stronger than the monopole (single charge) field.

B. The dipole field is weaker than the monopole field.

C. The dipole field is equal to the monopole field.

Continuous Distribution (P23.27)

∫Uniform volume charge density = q/V and dq = dV

Uniform surface charge density = q/A and dq = dA

Uniform linear charge density = q/l and dq = dl

Note: E depends only on the source charge distribution

Ch23.5 Electric Field of a Continuous Charge Distribution

dl = rd

dq = dl

r

dEx

dE

Ch23.27

Ch23.6 Electric

Field Lines

• Electric field lines give a visualization of the electric force field

• The field points along the line in the direction of the arrow

• Field lines leave + charges and end on – charges

• The number of lines is proportional to the source charge, so the density of lines is proportional to field strength

Electric Field Lines – Isolated Positive Point Charge

Ch23.6 Electric Field Lines

Electric Field Lines – Isolated Negative Point Charge

Electric Field Lines – Isolated Positive and

Negative Point Charges Compared

Electric Field Lines – Two Isolated and Separated Equal Positive Point Charges

Electric Field Lines – Isolated and Separated Equal Positive and Negative

Point Charges – Electric Dipole

Electric Field Lines – Two Parallel Oppositely, but Equally, Charged Plates - Capacitor

Electric Field Lines – Two Isolated Separated Charges of Opposite Sign and Different Magnitudes

P23.40 a) What is the ratio q2/q1? b) Signs of q1 and q2?

CT23.5

• 1

• 2

• 3

• 4

CT23.6

A. +,+

B. +,-

C. -,+

D.-,-

Ch23.7 Motion of Charged Particles in a Uniform Electric Field

Squeak Demo

Do P23.41

The coin doesn’t have to be charged for the cup to attract the coin. The charged cup can induce a polarization of the charge which results in an attraction. Common misconceptions - Charged objects only interact with other charged objects. Charged objects do not interact with uncharged (neutral) objects. Uncharged (neutral) is considered to be a third type of charge. Charged and uncharged objects attract each other because they are opposites. Correct answer