Chapter 17:Electric Forces

and Fields

Objectives

• Understand the basic properties of electric charge.

• Differentiate between conductors and insulators.

• Distinguish between charging by contact, charging by induction, and charging by polarization.

Electric Charge

• Ben Franklin: two kinds of charge, positive and negative

• opposite charges attract; like charges repel

• Law of Conservation of Charge: it can’t be destroyed, total is constant

• charge (q) is measured in coulombs (C)• electrons (–), protons (+)• Robert Millikan (1909): fundamental

charge = +/– 1.60 x 10-19 C

Transfer of Electric Charge

• charges move freely through conductors (typically metals, ionic solutions)

• charges do not move freely in insulators (most other substances)

Electric charge can be transferred 3 ways:• friction/contact• induction• polarization

Objectives

• Calculate electric force using Coulomb’s law.• Compare electric force with gravitational

force.

Coulomb’s Law

F Gm m

rG 1 22

F kq q

re 1 22

Law of Universal Gravitation

Coulomb’s Lawk = 8.99 x 109 Nm2/C2

Which is Stronger, Fe or FG?

• Compare the Fg and the Fe between the p+ and e- in a hydrogen atom (r = 53 pm).

Objectives

• Calculate electric field strength.• Draw and interpret electric field lines.• Identify the properties associated with a

conductor in electrostatic equilibrium.

Electric Fields

• Field lines show direction and strength of force (represented by the line density) acting on a charge

• E-field: (+) → (–)• units are N/C

F q E

EF

q

e

e

0

0

Electric Fields

The nucleus applies a force of 8.16 x 10-11N on the electron in a hydrogen atom. (a) What is the electric field strength at the position

of the electron?(b) What is the orbital period of the electron,

assuming it orbits in a circular path (it really doesn’t)?

Conductors in Electrostatic Equilibrium

electrostatic equilibrium: no net motion of charge(a) The total electric field inside a conductor equals zero.(b) Excess charge resides on the surface.(c) E-field lines extend perpendicular to the surface.(d) Charge accumulates at points.

Chapter 18: Electric Energy

and Capacitance

Objectives

• Understand the concept of electric potential energy (EPE).

• Calculate the DEPE when a charged particle is moved in a uniform electric field.

Electric Potential Energy (EPE)

PE m g hgrav PE q E delectric

g

E

• uniform field only!• displacement in direction of the field

EPE Problems

• What is the change in EPE if a proton is moved 2.5mm in the direction of a uniform 7.0 x1011 N/C electric field?

• What is the change in EPE if an electron is moved in the same direction?

Potential Difference (Voltage)• voltage (V) is EPE per

charge• 1 volt = 1 J/C• measured with a

voltmeter• voltage is like an

“electric pressure” that pushes charges

• batteries, outlets, generators, etc. supply voltage

PE m g h

PE

mg h

grav

grav

PE q E d

PE

qE d

vo ltagePE

qE d

V E d

electric

electric

electric

" "

(uniform field only)

Voltage Problems

What voltage exists in a 3.5 x10-6 N/C electric field between two points that are 0.25 m apart?

Capacitors• Capacitors store EPE between

two closely-spaced conductors (separated by an insulator).

• Capacitance is measured in farads (F). 1 F = 1 C/V

• Capacitors can discharge very quickly—producing short bursts of electrical current

CQ

VPE Q Velectric

12

Chapter 19:Electric Current and

Electric Power

Electric Current

Electric charges will flow between areas of different electric potential (voltage)

• electric current (I): a flow of electric charge• 1 ampere (A) = 1 C/s• measured with an ammeter• although electrons typically flow, current is defined as direction of positive flow (+ → –)• drift speed of e– in Cu at 10 A is only 0.00025 m/s• 0.005 A is painful and 0.070 A can kill you

Electric Resistance

• resistance (R): resistance to electron flow• measured in Ohms (Ω)• V ↑, I ↑• R ↑, I ↓

IV

R

A 2400-Ω resistor is attached to a 12-V power source. What is the current through the wire?

AC/DC• alternating current: electric field reverses periodically, current alternates direction (60 hz in USA)

• direct current: field is constant, current is constant• batteries produce DC• electric generators can make AC or DC

Electric Power and Energy

J

CV

J C V

J

s

C V

s

C

sV

W A V

P I Velec

Consider the units of voltage:

E I V telec

Electric power is transported at high voltage and low current to minimize “I2R loss.”

Power Problems

An electric oven operates on a 240 V circuit (not the regular 120 V). How much current flows through the element in the oven if the power usage is 3200 W?

At $0.06 / kW·hr, how much does it cost to operate a 280-W television for 2 hrs?

Objectives

• To understand the concepts of series and parallel circuits.

• To calculate the total resistance and current flowing through a circuit containing series and/or parallel circuits.

Series Circuit

Series Circuit

• Resistors (or loads) “in series” just combine to make a larger resistance.

• RT = R1 + R2 + R3 + …

• In a series circuit, if V = 12 V, R1 = 1 Ω, R2 = 2 Ω, and R3 = 3 Ω, what is RT and current?

• What is the “voltage drop” across each resistor?• Holiday lights are often in series: if one bulb

burns out, nothing works!

Parallel Circuit

Parallel Circuits

• Resistors in parallel provide additional paths for current to flow, so resistance decreases.

• 1/RT = 1/R1 + 1/R2 + 1/R3 + …

• In a parallel circuit, if V = 12 V, R1 = 1 Ω, R2 = 2 Ω, and R3 = 3 Ω, what is RT and IT flowing through the entire circuit? What is the current in each resistor? What is the voltage drop across each resistor?

• Household circuits are wired in parallel.

Voltage Drops

• The current flowing through a resistor depends on the voltage drop “across” the resistor.

• Series example: V = 12 V, R1 = 1 Ω, R2 = 2 Ω, and R3 = 3 Ω

• Parallel example: V = 12 V, R1 = 1 Ω, R2 = 2 Ω, and R3 = 3 Ω