Chapter 1
Electric Charge and Electric Field
Chapter 1 outline 1.1 Introduction 1.2 Electric charge 1.3 Movement of charges 1.4 electrostatic force 1.5 Electric fields 1.6 Principle of Superposition 1.7 Electric dipoles
PHY 3104
Physics II
SEM 1 2010-2011
Goals for Chapter 1 By the end of this topic, student will able : • To understand electric charge and see how charge behaves in conductors and insulators • To calculate force with Coulomb’s Law • To consider the electric field as a map of force on a test charge • To see how electric fields superimpose • To visualize and consider the path of electric field lines around a charge or charges • To see the unique applications of electric dipoles11 PHY 3104
Physics II
SEM 1 2010-2011
1.1 Introduction • Water pervades the science of chemistry and biology. It’s not only what we drink when we’re thirsty, but it’s been called “the universal solvent.” • Even if we were to only look at water, and water as a solvent, we would see a simple problem like salt dissolving in water is the interaction of electrostatic charges, of ions and dipoles. PHY 3104
Physics II
SEM 1 2010-2011
1.2 Electric charge • Glass rods, plastic tubes, silk, and fur can be used to demonstrate the movement of electrons and how their presence or absence make for powerful forces of attraction and repulsion.
PHY 3104
Physics II
SEM 1 2010-2011
The photocopier, a very clever tool • The world may have come to take copiers for granted, but they are amazing devices. They use charge to hold fine dust in patterns until the pattern may be transferred to paper and made permanent with heat.
PHY 3104
Physics II
SEM 1 2010-2011
How is the atom arranged? Why is it easiest to move electrons?
• Visualize a football stadium as an atom. • Electrons would be garden peas in the highest seats with charge of −1. • Protons would be basketballs or melons with charge of +1, and neutrons would reside about the protons with no charge. • All of the protons and neutrons could be in a small basket on the 50-yard line. PHY 3104
Physics II
SEM 1 2010-2011
Consider lithium as a cation, an anion, and a neutral • Let’s study the subatomic arrangement of lithium with all charges balanced and the way only electrons move to make the atom an ion (+ or −).
PHY 3104
Physics II
SEM 1 2010-2011
1.3 Movement of charges—charging by conduction • Materials that allow easy passage of charge are called conductors. • Materials that resist electronic flow are called insulators. • The motion of electrons through conducts and about insulators allows us to observe “opposite charges attract” and “like charges repel.”
PHY 3104
Physics II
SEM 1 2010-2011
Electrons move freely and charges may be induced • Take a child’s toy, a rubber balloon. If you rub the balloon vigorously on a fuzzy sweater then bring the balloon slowly toward a painted concrete or plaster wall, the balloon will stick to the wall and remain for some time. • The electrostatic force between static electrons and the induced positive charge in the wall attract more strongly than the weight of the balloon.
PHY 3104
Physics II
SEM 1 2010-2011
Static electricity about an insulator can shift • The motion of static charges about a plastic comb and light bits of paper can cause attractive forces strong enough to overcome the weight of the paper.
PHY 3104
Physics II
SEM 1 2010-2011
Charges will “seek” motion to ground • An uncharged conductor can attract the charge imparted to paint droplets.
PHY 3104
Physics II
SEM 1 2010-2011
1.4 Charles Coulomb determined the electrostatic force law • Coulomb’s Law allows the calculation of electrostatic attraction or repulsion.
PHY 3104
Physics II
SEM 1 2010-2011
Examples of electrical force calculated—Ia
PHY 3104
Physics II
SEM 1 2010-2011
Examples of electrical force calculated—Ib
PHY 3104
Physics II
SEM 1 2010-2011
Examples of electrical force calculated—IIa
PHY 3104
Physics II
SEM 1 2010-2011
Examples of electrical force calculated—IIb
PHY 3104
Physics II
SEM 1 2010-2011
1.5 Electric fields may be mapped by force on a test charge •
If one measured the force on a test charge at all points relative to another charge or charges, an electric field may be mapped.
•
This experiment is often done in one’s mind (called a “gedanken experiment”).
•
The electric force on a charged body is exerted by the electric field created by other charged bodies.
•
Definition of electric field as electric force per unit charge
FO E= qO
PHY 3104
Physics II
SEM 1 2010-2011
Electric fields I—the point charge • Fields of force may be sketched for different arrangements of charge. • Consider the electric field E produced at point P by an isolated point charge q at S.
1 qqo Fo = 4πε o r 2 E=
PHY 3104
Physics II
1 q rˆ 2 4πε o r SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
Electric fields II—charges in motion within a field Example 21.7 When the terminals of a battery are connected to two large parallel conducting plates, the resulting charges on the plates cause an electric field E in the region between the plates that is very nearly uniform. If the plates are horizontal and separated by 1.0cm and the plates are connected to a 100 volt battery, the magnitude of the field is E=1.0 x 10 4 N/C. Suppose the direction of E is vertically upward, as shown in figure (a) If an electron is release from rest at the upper plate, what is its acceleration? (b) What speed and kinetic energy does the electron acquire while traveling 1.0 cm to lower plate? (c) How much time is required for it to travel this distance? An electron has charge –e = – 1.60x10 – 19 C and mass m=9.11x10–31kg. PHY 3104
Physics II
SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
Electric fields II—charges in motion within a field
PHY 3104
Physics II
SEM 1 2010-2011
1.6 Principle of Superposition For example the net force F1 exerted on q1 by q2 and q3 is equal to: F1 = F12 + F13 Here F12 and F13 are the forces exerted on q1 by q2 and q3 , respectively. In general the force exerted on q1 by n charges is given by the equation: n F1 = F12 + F13 + F14 + ... + F1n = ∑ F1i i=2
One must remember that F12 , F13 , ...are vectors and thus we must use use vector addition. Inthe example of fig.f we have:
F1 = F12 + F14
The net electric force exerted by a group of charges is equal to the vector sum of the contribution from each charge.
PHY 3104
Physics II
SEM 1 2010-2011
• Similar in electric field, the net electric field exerted by a group of charges is equal to the vector sum of the contribution from each charge. • This is the priciple of superposition of electric fields
F E = = E1 + E2 + E3 + .... q
PHY 3104
Physics II
SEM 1 2010-2011
Electric fields add as vectors Example 21.9 Point charges q1 and q2 of +12 nC and –12nC, respectively, are placed 0.10m apart. This combination of two charges with equal magnitude and opposite sign is called an electric dipole. Compute the electric field cause by q1, the field caused by q2, and the total field (a) at point a, (b) at point b and (c) at point c.
PHY 3104
Physics II
SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
Electric field lines map out regions of equivalent force I
PHY 3104
Physics II
SEM 1 2010-2011
P
1.7
Electric Dipole
+q
A system of two equal charges of opposite sign
d -q
+q/2
+q/2
-q
( ±q )
placed at a distance d is known as an "electric
dipole". For every electric dipole we associate a vector known as "the electric dipole moment" (symbol p )defined as follows: The magnitude p = qd The direction of p is along the line that connects the two charges and points from - q to + q. Many molecules have a built-in electric dipole moment. An example is the water molecule (H 2 O) The bonding between the O atom and the two H atoms involves the sharing of 10 valence electrons (8 from O and 1 from each H atom)
PHY 3104
Physics II
SEM 1 2010-2011
Consider force and torque on a dipole • Both force F(+) and F(–) have magnitude qE, but their direction are opposite. • Therefore, the net force on an electric dipole in a uniform external electric field is zero. • The individual torque (τ = F. x, F and x is perpendicular) is
τ = (qE )(d sin φ )
τ = p× E
• The product of the charge q • and the separation d is the magnitude of a quantity called the electric dipole moment, denoted by p:
p = qd Unit : Coulomb meter (C.m) PHY 3104
Physics II
SEM 1 2010-2011
Potential Energy of an Electric Dipole When a dipole changes direction in an electric field, the electricfield torque does work on it, with a corresponding change in potential energy.
dW = τdφ = − pE sin φdφ
In a finite displacement from φ1 to φ2, the total work is φ2
W = ∫ (− pE sin φ )dφ = −( pE sin φ2 − pE sin φ1 ) φ1
W = −(U 2 − U1 ) Therefore
U = − pE sin φ PHY 3104
Physics II
or
U = −p•E SEM 1 2010-2011
PHY 3104
Physics II
SEM 1 2010-2011
Summary • Properties of Electric charge, conductors, and insulators .
• Coulomb’s law: Coulomb’s law is the basic law of interaction for point electric charges. 1 q1 q2 F= 4πε 0 r 2 PHY 3104
Physics II
1 = 8.988 × 109 N ×m 2 /C 2 4πε 0 SEM 1 2010-2011
• Electric field : a vector quantity, is the force per unit charge exerted on a test charge at any point • Superposition of electric fields: The principle of superposition of electric fields states that the electric field of any combination of charges is the vector sum of the fields caused by the individual charges. PHY 3104
Physics II
F0 E= q0
1 q E= rˆ 2 4πε 0 r
SEM 1 2010-2011
•
Electric field lines: Field lines provide a graphical representation of electric fields. –
At any point on a field line, the tangent to the line is in the direction of at that point. The number of lines per unit area (perpendicular to their direction) is proportional to the magnitude of at the point.
τ = (qE )(d sin φ ) τ = p× E U = −p•E PHY 3104
Physics II
SEM 1 2010-2011