electric charge and electric field
TRANSCRIPT
Chapter 21Electric Charge and
Electric Field
Objects can be charged by rubbing
21.1 Static Electricity; Electric Charge and its Conservation
Charge comes in two types, positive and negative; like charges repel and opposite charges attract
21.1 Static Electricity; Electric
Charge and its Conservation
Electric charge is conserved – the arithmetic sum of the total charge cannot change in any interaction.
21.1 Static Electricity; Electric Charge and its Conservation
Conductor:
Charge flows freely
Metals
Insulator:
Almost no charge flows
Most other materials
Some materials are semiconductors.
21.3 Insulators and Conductors
Metal objects can be charged by conduction:
21.4 Induced Charge; the Electroscope
They can also be charged by induction, either while connected to ground or not:
21.4 Induced Charge; the Electroscope
Nonconductors won’t become charged by conduction or induction, but will experience charge separation:
21.4 Induced Charge; the Electroscope
The electroscope can be used for detecting charge:
21.4 Induced Charge; the Electroscope
The electroscope can be charged either by conduction or by induction.
21.4 Induced Charge; the Electroscope
The charged electroscope can then be used to determine the sign of an unknown charge.
21.4 Induced Charge; the Electroscope
Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.
21.5 Coulomb’s Law
The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same.
21.5 Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s law is then:
k = 8.099 x 109 N·m2/C2
Charges produced by rubbing are typically around a microcoulomb:
1 μC = 10-6 C
21.5 Coulomb’s Law
Charge on the electron:
e = 1.602 x 10-19 C
Electric charge is quantized in units of the electron charge.
21.5 Coulomb’s Law
21.5 Coulomb’s Law
Conceptual Example 21-1: Which charge exerts the greater force?
Two positive point charges, Q1 = 50 μC and Q2 = 1 μC, are separated by a distance l. Which is larger in magnitude, the force that Q1 exerts on Q2 or the force that Q2 exerts on Q1?
21.5 Coulomb’s LawExample 21-2: Three charges in a line.
Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges.
21.5 Coulomb’s LawExample 21-3: Electric force using vector components.
Calculate the net electrostatic force on charge Q3 shown in the figure due to the charges Q1 and Q2.
21.5 Coulomb’s Law
Conceptual Example 21-4: Make the force on Q3 zero.
In the figure, where could you place a fourth charge, Q4 = -50 μC, so that the net force on Q3 would be zero?
The electric field is defined as the force on a small charge, divided by the magnitude of the charge:
21.6 The Electric Field
21.6 The Electric Field
An electric field surrounds every charge.
Force on a point charge in an electric field:
21.6 The Electric Field
21.6 The Electric Field
Example 21-6: Electric field of a single point charge.
Calculate the magnitude and direction of the electric field at a point P which is 30 cm to the right of a point charge Q = -3.0 x 10-6 C.
21.6 The Electric Field
Example 21-8: E above two point charges.
Calculate the total electric field (a) at point A and (b) at point B in the figure due to both charges, Q1 and Q2.
Problem solving in electrostatics: electric forces and electric fields
1. Draw a diagram; show all charges, with signs, and electric fields and forces with directions
2. Calculate forces using Coulomb’s law
3. Add forces vectorially to get result
4. Check your answer!
21.6 The Electric Field
The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.
21.8 Field Lines
The number of field lines starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge.
The electric field is stronger where the field lines are closer together.
21.8 Field Lines
Electric dipole: two equal charges, opposite in sign:
21.8 Field Lines
The electric field between two closely spaced, oppositely charged parallel plates is constant.
21.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the field; the field is tangent to the line.
2. The magnitude of the field is proportional to the density of the lines.
3. Field lines start on positive charges and end on negative charges; the number is proportional to the magnitude of the charge.
21.8 Field Lines
The static electric field inside a conductor is zero – if it were not, the charges would move.
The net charge on a conductor resides on its outer surface.
21.9 Electric Fields and Conductors
The electric field is perpendicular to the surface of a conductor – again, if it were not, charges would move.
21.9 Electric Fields and Conductors
21.9 Electric Fields and Conductors
Conceptual Example 21-14: Shielding, and safety in a storm.
A neutral hollow metal box is placed between two parallel charged plates as shown. What is the field like inside the box?
21.10 Motion of a Charged Particle in an Electric Field
The force on an object of charge q in an electric field E is given by:
F = qE
Therefore, if we know the mass and charge of a particle, we can describe its subsequent motion in an electric field.
21.10 Motion of a Charged Particle in an Electric Field
Example 21-16: Electron moving perpendicular to E.
Suppose an electron traveling with speed v0 = 1.0 x 107 m/s enters a uniform electric field E, which is at right angles to v0 as shown. Describe its motion by giving the equation of its path while in the electric field. Ignore gravity.
Chapter 23Electric Potential
The electrostatic force is conservative – potential energy can be defined
Change in electric potential energy is negative of work done by electric force:
23.1 Electrostatic Potential Energy and Potential Difference
Electric potential is defined as potential energy per unit charge:
Unit of electric potential: the volt (V).
1 V = 1 J/C.
23.1 Electrostatic Potential Energy and Potential Difference
Analogy between gravitational and electrical potential energy:
23.1 Electrostatic Potential Energy and Potential Difference
23.1 Electrostatic Potential Energy and Potential Difference
Electrical sources such as batteries and generators supply a constant potential difference. Here are some typical potential differences, both natural and manufactured:
An equipotential is a line or surface over which the potential is constant.
Electric field lines are perpendicular to equipotentials.
The surface of a conductor is an equipotential.
23.5 Equipotential Surfaces
23.5 Equipotential Surfaces
Example 23-10: Point charge equipotential surfaces.
For a single point charge with Q = 4.0 × 10-9C, sketch the equipotential surfaces (or lines in a plane containing the charge) corresponding to V1 = 10V, V2 = 20V, and V3 = 30V.
23.5 Equipotential SurfacesEquipotential surfaces are always perpendicular to field lines; they are always closed surfaces (unlike field lines, which begin and end on charges).
• INTRODUCTIONIn the past chapters we have been discussing interactions of electric charges “at rest” (electrostatic).
Now we are ready to study charges “in motion”.
An electric current consists of motion of charges charges from one region to another.
When this motion of charges takes place within a conductor that forms a closed path, the path is called an electric circuit.
Chapter 18ELECTRIC CURRENTS
THE ELECTRIC CURRENTChapter 18-2
We can also define current through the area as the net charge flowing through the area per unit time.
dt
dQI
CURRENT (Electric Current) It is the rate of flow of electric charge through a cross-
sectional area.
OHM’S LAW:RESISTANCE AND RESISTORS
• RESISTANCE– The proportionality of J to E for a metallic
conductor at constant temperature was discovered by G.S. Ohm.
Chapter 18-3
IRV
A
LR
For Ohmic materials
(those that obey Ohm’s law), the potential V is proportional to the current I.
The behavior will always trace a linear relationship.
OHM’S LAW:RESISTANCE AND RESISTORS
• RESISTOR
Chapter 18-3
A
LR
Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B?
ELECTRIC POWERChapter 18-5
VIdt
dWP
R
VRIVIP
22
Power dissipated in a conductor
Power dissipated in a resistor
A CIRCUIT is a closed conducting path current flow all the way around.
• The POWER is the work done per unit time or the time rate of energy transfer
EMF AND TERMINAL VOLTAGEChapter 19-1
Ideal Emf SourceReal Battery
Electromotive Force (emf) Source It is a device that supplies electrical
energy to maintain a steady current in a circuit.
It is the voltage generated by a battery.
IrVab ε
εabV
RESISTORS INSERIES AND PARALLEL
nRRRR ...21eq
Chapter 19-2
RESISTORS IN SERIES The magnitude of the charge is constant. Therefore, the
flow of charge, current I is also constant. The potential of the individual resistors are in general
different.
The equivalent resistance of resistors in series equals the sum of their individual resistances.
RESISTORS IN PARALLEL The upper plates of the capacitors are connected together to
form an equipotential surface – they have the same potential. The lower plate also have equal potential.
The charges on the plates may not necessarily be equal.
RESISTORS INSERIES AND PARALLEL
1
21eq
1...
11
nRRRR
Chapter 19-2
RESISTORS INSERIES AND PARALLEL
Chapter 19-2
Problem set
• Three charged particles are placed at the corners of an equilateral triangle of side 1.20m (shown in the figure). (a) Calculate the magnitude and direction of the net force and electric field on each due to the other two. (b) calculate for the electric potential at the midpoint of the triangle.
• (a)What is the equivalent resistance of the circuit shown.(b) What is the current in the 18-ohm resistor, 12-ohm resistor (c) power dissipation in the 4.5 –ohm reistor.