chapter 1

ELECTRIC FIELD

LEARNING OBJECTIVE

Able to: 1. Describe the concept of electric charge.2. List the differences and similarities between conductors and insulators. 3. Describe the process of charging by induction. 4. Describe the electric force 5. Calculate the force that charges exert on each other. 6. Determine the direction of the electric force for different source charges.

electric charges

• Two kinds of electric charges : positive and negative
• Negative charges - electrons.
• Positive charges - protons.

electric charges

• The rubber rod is negatively charged
• The glass rod is positively charged
• The two rods will attract.

electric charges

• The rubber rod is negatively charged
• The second rubber rod is also negatively charged.
• The two rods will repel.

CONCEPT TEST

Object A has a charge of +2 µC, and object B has a charge of +6 µC.Which statement is true about the electric forces on the objects?

A. FAB = -3FBA B. FAB = -FBA C. 3FAB = 2FBA D. FAB = 3FBA E. FAB = FBA F. 3FAB = FBA

CONCEPT TEST

Object A has a charge of +2 µC, and object B has a charge of +6 µC.Which statement is true about the electric forces on the objects?

A. FAB = -3FBA B. FAB = -FBA C. 3FAB = 2FBA D. FAB = 3FBA E. FAB = FBA F. 3FAB = FBA

CONCEPT TEST

Three objects are brought close to one another, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. Which of the following are necessarily true?

A. Objects A and C possess charges of the same signB. Objects A and C possess charges of opposite sign. C. All three objects possess charges of the same sign. D. One object is neutral. E. Additional experiments must be performed to determine any information about the charges on the objects.

CONCEPT TEST

Three objects are brought close to one another, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. Which of the following are necessarily true?

A. Objects A and C possess charges of the same signB. Objects A and C possess charges of opposite sign. C. All three objects possess charges of the same sign. D. One object is neutral. E. Additional experiments must be performed to determine any information about the charges on the objects.

CONSERVATION OF ELECTRIC CHARGES

• Electric charge is always conserved in an isolated system.
• Charge is not created in the process of rubbing two objects together.
• The electrification is due to a transfer of charge from one object to another.

CONSERVATION OF electric charges

• A glass rod is rubbed with silk.
• Electrons are transferred from the glass to the silk.
• Each electron adds a negative charge to the silk.
• An equal positive charge is left on the rod.

Quantization of Electric Charges

• The electric charge, q, is said to be quantized.
• q is the standard symbol used for charge as a variable.
• Electric charge exists as discrete packets.
• q = +-Ne
• N is an integer e is the fundamental unit of charge
• |e| = 1.6 x 10-19 C
• Electron: q = -e
• Proton: q = +e

conductor

• Electrical conductors are materials in which some of the electrons are free electrons.
• Free electrons are not bound to the atoms --> move freely through the material.

• When a good conductor is charged by rubbing in a small region, the charge readily distributes over the entire surface of the material.

insulator

• Electrical insulators are materials in which all of the electrons are bound to atoms.
• These electrons cannot move relatively freely through the material.

• When a good insulator is charged by rubbing, only the area become charged & unable to move to other regions of the material.

semiconductor

• The electrical properties are somewhere between those of insulators and conductors.
• Examples: silicon and germanium.
• used in fabrication of electronic chips.
• The electrical properties changed by the addition of certain atoms to the material.

charging by induction, 1

Charging by induction requires no contact with the object inducing the charge. A:

• Assume we start with a neutral metallic sphere.
• The sphere has the same number of positive and negative charges.

charging by induction, 2

• B:
• A charged rubber rod is placed near the sphere. It does not touch the sphere.
• The electrons in the neutral sphere are redistributed.
• C:
• The sphere is grounded. Some electrons can leave the sphere through the ground wire.

charging by induction, 3

• The ground wire is removed.
• There will now be more positive charges.
• The charges are not uniformly distributed.
• The positive charge has been induced in the sphere.

charging by induction, 4

• The rod is removed.
• The electrons remaining on the sphere redistribute themselves.
• There is still a net positive charge on the sphere. The charge is now uniformly distributed.
• Note the rod lost none of its negative charge during this process.

Charge Rearrangement in Insulators

• A process similar to induction can take place in insulators.
• The charges within the molecules of the material are rearranged.
• The positive charges on the surface of the object and the negative charges on the surface of the insulator --> attractive force between them

concept test

Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors?

concept test

Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors?

concept test

When a negatively charged object is placed inside an uncharged hollow conductor, a negatively charged pith ball is repelled by the arrangement (see a). The uncharged hollow conductor is now grounded (see b). What happens to the pith ball?

concept test

When a negatively charged object is placed inside an uncharged hollow conductor, a negatively charged pith ball is repelled by the arrangement (see a). The uncharged hollow conductor is now grounded (see b). What happens to the pith ball?

coulomb experiment

Charles Augustin de Coulomb - First theoretical study of electric forces between charged bodies (1784) - Torsion balance to measure the variation in force with separation & quantity of charge

coulomb's law

Charles Coulomb found that The electrical forces is: - proportional to the product of charges, q1 and q2 - inversely proportional to the square of the distance r between the charges

French physicist (1736-1806)

Coulomb's law

" The force of attraction or repulsion between two point charges is directly proportional of the two charges and inversely proportional to the square of the distance between them. "

Coulomb’s Law Equation

Coulomb’s Law Equation

particle summary

The electron and proton are identical in the magnitude of their charge, but very different in mass. The proton and the neutron are similar in mass, but very different in charge.

the hydrogen atom

The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3 x 10-11 m. Find the magnitudes of the electric force and the gravitational force between the two particles. (Given: ke=8.988 x 109N. m2/C2G =6.674 x 10-11 N.m2/kg2)

the hydrogen atom

Use Coulomb's Law

Use Newton’s law of universal gravitation

The gravitational force between charged particles is negligible compared with electric force

Vector Nature of Electric Forces

Electric force exerted by a charge q1 on a second charge q2, written as F12

Vector Nature of Electric Forces

Vector Nature of Electric Forces

• Two point charges are separated by a distance r.
• Unlike charges produce an attractive force between them.
• With unlike signs for the charges, the product q1q2 is negative and the force is attractive.
• The sign of the product of q1q2 gives the relative direction of the force between q1 and q2.
• The absolute direction is determined by the actual location of the charges.

CONCEPT TEST

• A proton and an electron are held apart a distance of 1m and then released. As they approach each other, what happens to the force between them?

CONCEPT TEST

• A proton and an electron are held apart a distance of 1m and then released. As they approach each other, what happens to the force between them?

MULTIPLE CHARGES

The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges For example, if four charges are present, the resultant force exerted by particles 2, 3, and 4 on particle 1 is

Tips on solving problem

1. Decide which charge to be addressed2. Determine the direction of the force on that charge due to the other charge 3. Direction determined by the laws for attraction and repulsion -like charges repel, unlike charges attract. The charges must in Coulombs, distance must in meters if the force is in Newtons

ExAMPLE 1

Two charges, q1 = -8µC and q2 =+12µC, are placed 12 cm apart in the air, What is the resultant force on a third charge, q3 = -4µC, placed midway between the two charges?

Electrical Force with Other Forces

• Since they are separated, they exert a repulsive force on each other.
• Model each sphere as a particle in equilibrium.
• Proceed as usual with equilibrium problems, noting one force is an electrical force.

Electrical Force with Other Forces

• The force diagram includes the components of the tension, the electrical force, and the weight.
• Solve for |q|

Example 2

Three charges, q1= +4 x 10-9C, q2= -6 x 10-9C and q3=-8 x 10-9C are arranged as shown in Fig. 1. What is the resultant force on q3 due to the other two charges?

Solution:

1) Find F13 and F23

2) Find F13 and F23 at each component

3) Find the magnitude of resultant force on q3 and direction

learning objective

• Explain the purpose of the electric field
• Describe the properties of the electric field
• Calculate the field of a collection of source charges of either sign
• Explain what a continuous source charge distribution and how it is related to the concept of quantization of charge
• Describe line charges, surface charges, and volume charges
• Calculate the field of a continuous source charge distribution of either sign

Electric field- introduction

The electric force is a field force. Field forces can act through space.

• The effect is produced even with no physical contact between objects.

Faraday developed the concept of a field in terms of electric fields.

Electric field- Definition

An electric field is said to exist in the region of space around a charged object.

• This charged object is the source charge.

When another charged object, the test charge, enters this electric field, an electric force acts on it.

Electric field

Electric field in the vicinity of positive charge would be outward (away from charge) Electric field in the vicinity of negative charge would be inward (toward the charge)

Electric field- Definition

The electric field is defined as the electric force on the test charge per unit charge. The electric field vector, E , at a point in space is defined as the electric force acting on a positive test charge, qo, placed at that point divided by the test charge:

Electric field

E is the field produced by some charge or charge distribution, separate from the test charge. The existence of an electric field is a property of the source charge. The presence of the test charge is not necessary for the field to exist. The test charge serves as a detector of the field.

Electric field

The direction of E is that of the force on a positive test charge. The SI units of E are N/C. We can also say that an electric field exists at a point if a test charge at that point experiences an electric force.

RELATIONSHIP BETWEEN F AND E

• If q is placed in Electric field, it experience electric force of

• If q is positive, the force and the field are in the same direction.
• If q is negative, the force and the field are in opposite directions.

EXAMPLE

The electric field intensity between two plates in Fig. 2 is constant and directed downward. The magnitude of the electric field intensity is 6 x 104 N/C. What are the magnitude and the direction of the electric force exerted on an electron projected horizontally between the two plates?

F= qeE = (1.6 x 10 -19) (6 x 104 N/C) = 9.6 x 10-15N (upward)

Fig. 2

Electric Field, Vector Form

Remember Coulomb’s law, between the source and test charges, can be expressed as Then, the electric field will be

Electric Field between 2 charges

More About Electric Field Direction

a) q is positive, the force is directed away from qb) The direction of the field is also away from the positive source charge c) q is negative, the force is directed toward q d) The field is also toward the negative source charge.

CONCEPT TEST

There is an electric field at point P. A very small positive charge is placed at this point and experiences a force. Then the positive charge is replaced by a very small negative charge that has a magnitude different from that of the positive charge. Which one of the following statements is true concerning the forces that these charges experience at P?

A. They are identical. B. They have the same magnitude but different directions. C. They have different magnitudes but the same direction. D. They have different magnitudes and different directions.

CONCEPT TEST

There is an electric field at point P. A very small positive charge is placed at this point and experiences a force. Then the positive charge is replaced by a very small negative charge that has a magnitude different from that of the positive charge. Which one of the following statements is true concerning the forces that these charges experience at P?

A. They are identical. B. They have the same magnitude but different directions. C. They have different magnitudes but the same direction. D. They have different magnitudes and different directions.

CONCEPT TEST

You are sitting a certain distance from a point charge, and you measure an electric field of E0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now?

CONCEPT TEST

You are sitting a certain distance from a point charge, and you measure an electric field of E0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now?

Remember that the electric field is: E = kQ/r2.Doubling the charge puts a factor of 2 in the numerator, but doubling the distance puts a factor of 4 in the denominator, because it is distance squared!! Overall, that gives us a factor of 1/2.

Electric Fields from Multiple Charges

At any point P, the total electric field due to a group of source charges equals the vector sum of the electric fields of all the charges.

Electric Fields due to two charges

Charges q1 and q2 are located on the x axis, at distances a and b, respectively, from the origin as shown in Fig. 3. a) Find the components of the net electric field at the point P, which is at position (0, y). b)Evaluate the electric field at point P in the special case that Iq1I = Iq2I and a = b.

Fig. 3

a) Find the components of the net electric field at the point P, which is at position (0, y).

a) Find the components of the net electric field at the point P, which is at position (0, y).

Fig. 3

a) Find the components of the net electric field at the point P, which is at position (0, y).

b)Evaluate the electric field at point P in the special case that Iq1I = Iq2I and a = b.

CONTINUOUS CHARGE DISTRIBUTION

• used to calculate electric field due to small number of charges

• continuous distribution of charge rather than collection of discrete charges.

• The system of closely spaced charges is equivalent to a total charge that is continuously distributed along some line, over some surface, or throughout some volume.

CONTINUOUS CHARGE DISTRIBUTION

• Procedure:
• Divide the charge distribution into small elements, each of which contains Δq.
• Calculate the electric field due to one of these elements at point P.
• Evaluate the total field by summing the contributions of all the charge elements.

CONTINUOUS CHARGE DISTRIBUTION

For the individual charge elements Because the charge distribution is continuous

CHARGE DENSITIES

Volume charge density: when a charge is distributed evenly throughout a volume ρ ≡ Q / V with units C/m3 Surface charge density: when a charge is distributed evenly over a surface area σ ≡ Q / A with units C/m2 Linear charge density: when a charge is distributed along a line λ ≡ Q / ℓ with units C/m

AMOUNT OF CHARGE IN SMALL VOLUME

If the charge is nonuniformly distributed over a volume, surface, or line, the amount of charge, dq, is given by

• For the volume: dq = ρ dV
• For the surface: dq = σ dA
• For the length element: dq = λ dℓ

Problem-Solving Strategy

Conceptualize- Establish a mental representation of the problem. - Image the electric field produced by the charges or charge distribution. Categorize - Individual charge? - Group of individual charges? - Continuous distribution of charges?

Problem-Solving Strategy, cont

• Analyze
• Analyzing a group of individual charges:

• Use the superposition principle, find the fields due to the individual charges at the point of interest and then add them as vectors to find the resultant field.
• Be careful with the manipulation of vector quantities.

• Analyzing a continuous charge distribution:

• The vector sums for evaluating the total electric field at some point must be replaced with vector integrals.
• Divide the charge distribution into infinitesimal pieces, calculate the vector sum by integrating over the entire charge distribution.

• Symmetry:
• Take advantage of any symmetry to simplify calculations

Problem-Solving Strategy, cont

• Finalize

• Check to see if the electric field expression is consistent with your mental representation.

• Check to see if the solution reflects any symmetry present.

• Image varying parameters to see if the mathematical result changes in a reasonable way.

example- charged disk

The disk has a radius R and a uniform charge density σ.Choose dq as a ring of radius r. The ring has a surface area 2πr dr. Integrate to find the total field.

(uniform ring)

concept test

Assume a uniformly charged ring of radius R and charge Q produces an electric field Ering at a point P on its axis, at distance x away from the center of the ring. Now the same charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius. How does the field Edisk produced by the disk at P compare with the field produced by the ring at the same point?

concept test

Assume a uniformly charged ring of radius R and charge Q produces an electric field Ering at a point P on its axis, at distance x away from the center of the ring. Now the same charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius. How does the field Edisk produced by the disk at P compare with the field produced by the ring at the same point?

learning objective

• Explain the purpose of an electric field diagram.
• Describe the relationship between a vector diagram and a field line diagram.
• Explain the rules for creating a field diagram and why these rules make physical sense.
• Sketch the field of an arbitrary source charge.
• Determine the path of a charged object moving inside an electric field.

electric field lines

• The electric field vector is tangent to the electric field line at each point.
• The line has a direction that is the same as that of the electric field vector.
• The number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that region.

electric field lines

• The density of lines through surface A is greater than through surface B.
• The magnitude of the electric field is greater on surface A than B.
• The lines at different locations point in different directions.
• This indicates the field is nonuniform.

Electric Field Lines, Positive Point Charge

• The field lines radiate outward in all directions.
• In 3D, the distribution is spherical.
• The lines are directed away from the source charge.
• A positive test charge repelled away from the positive source charge.

Electric Field Lines, NEGATIVE Point Charge

• The field lines radiate inward in all directions.
• The lines are directed toward the source charge.
• A positive test charge attracted toward the negative source charge.

CONCEPT TEST

Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect?

CONCEPT TEST

Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect?

Electric Field Lines – Rules for Drawing

• The lines must begin on a positive charge and terminate on a negative charge.

• In the case of an excess of one type of charge, some lines will begin or end infinitely far away.

• The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.

• No two field lines can cross.

• Remember field lines are not material objects, they are a pictorial representation used to qualitatively describe the electric field.

Electric Field Lines – DIPOLE

• The charges are equal and opposite.

• The number of field lines leaving the positive charge equals the number of lines terminating on the negative charge.

Electric Field Lines – LIKE CHARGES

• The charges are equal and positive.
• The same number of lines leave each charge since they are equal in magnitude.
• At a great distance, the field is approximately equal to that of a single charge of 2q.
• Since there are no negative charges available, the field lines end infinitely far away.

Electric Field Lines – UNEQUAL CHARGES

• The positive charge is twice the magnitude, +2q of the negative charge, -q.

• The number of lines leaving +2q is twice the number terminate at -q.

• Only half the line reach -q, the remaining assume at infinity

CONCEPT TEST

Consider the electric field lines drawn for a configuration of two charges. Several locations are labelled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest.

CONCEPT TEST

Consider the electric field lines drawn for a configuration of two charges. Several locations are labelled on the diagram. Rank these locations in order of the electric field strength - from smallest to largest.

Electric field strength is greatest where the lines are closest together and weakest where lines are furthest apart.

CONCEPT TEST

Observe the electric field lines below. Rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge

CONCEPT TEST

Observe the electric field lines below. Rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge

Motion of Charged Particles

When a charged particle is placed in an electric field, it experiences an electrical force. If this is the only force on the particle, it must be the net force. The net force will cause the particle to accelerate according to Newton’s second law.

Motion of Charged Particles

• If the field is uniform, then the acceleration is constant.

• The particle under constant acceleration model can be applied to the motion of the particle.

• The electric force causes a particle to move according to the models of forces and motion.

• If the particle has a positive charge, its acceleration is in the direction of the field. If the particle has a negative charge, its acceleration is in the direction opposite the electric field.

Electron in a Uniform Field, Example

• The electron is projected horizontally into a uniform electric field.

• The electron undergoes a downward acceleration.

• It is negative, so the acceleration is opposite the direction of the field.

• Its motion is parabolic while between the plates.

THANKS