15_electric charge-forces-fields

Lecture Outline

Chapter 15

College Physics, 7th Edition

Wilson / Buffa / Lou

© 2010 Pearson Education, Inc.

Chapter 15Electric Charge, Forces, and

Fields

© 2010 Pearson Education, Inc.c

Units of Chapter 15

Electric Charge

Electrostatic Charging

Electric Force

Electric Field

Conductors and Electric Fields

Gauss’s Law for Electric Fields: A Qualitative Approach


15.1 Electric Charge

Electric charge is a fundamental property of matter; electric charges may be positive or negative.

The atom consists of a small positive nucleus surrounded by a negative electron cloud.



Like charges repel; unlike charges attract.



SI unit of charge: the coulomb, C. All charges are integer multiples of the charge on the electron:



Charge is conserved:

The net charge of an isolated system remains constant.


15.2 Electrostatic Charging

Conductors transmit charges readily.

Semiconductors are intermediate; their conductivity can depend on impurities and can be manipulated by external voltages.

Insulators do not transmit charge at all.


15.2 Electrostatic ChargingAn electroscope may be used to determine if an object is electrically charged.



Charging by friction: This is the process by which you get “charged up” walking across the carpet in the winter. It is also the process that creates “static cling” in your laundry, and makes it possible for you to rub a balloon on your hair and then stick the balloon to the wall.



An electroscope can be given a net charge by conduction—when it is touched with a charged object, the excess charges flow freely onto the electroscope.



An electroscope may also be charged by induction, if there is a way of grounding it while charge is being induced.



Charge may also be moved within an object—without changing its net charge—through a process called polarization.


Question 15.1a Electric Charge I

a) one is positive, the other

is negative

b) both are positive

c) both are negative

d) both are positive or both

are negative

Two charged balls are Two charged balls are

repelling each other as repelling each other as

they hang from the ceiling. they hang from the ceiling.

What can you say about What can you say about

their charges?their charges?

Question 15.1a Electric Charge I

The fact that the balls repel each

other can tell you only that they

have the same chargesame charge, but you do

not know the sign. So they can

be either both positive or both

negative.

a) one is positive, the other

is negative

b) both are positive

c) both are negative

d) both are positive or both

are negative

Two charged balls are Two charged balls are

repelling each other as repelling each other as

they hang from the ceiling. they hang from the ceiling.

What can you say about What can you say about

their charges?their charges?

Follow-upFollow-up:: What does the picture look like if the two balls are oppositely What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral?charged? What about if both balls are neutral?

a) have opposite charges

b) have the same charge

c) all have the same charge

d) one ball must be neutral (no charge)

From the picture, From the picture,

what can you what can you

conclude about conclude about

the charges?the charges?

Question 15.1b Electric Charge II

a) have opposite charges

b) have the same charge

c) all have the same charge

d) one ball must be neutral (no charge)

From the picture, From the picture,

what can you what can you

conclude about conclude about

the charges?the charges?

The GREEN and PINK balls must

have the same charge, since they

repel each other. The YELLOWYELLOW

ball also repels the GREEN, so it

must also have the same charge

as the GREEN (and the PINK).

Question 15.1b Electric Charge II

Question 15.2a Conductors I

a) positive

b) negative

c) neutral

d) positive or neutral

e) negative or neutral

A metal ball hangs from the ceiling

by an insulating thread. The ball is

attracted to a positive-charged rod

held near the ball. The charge of

the ball must be:

Clearly, the ball will be attracted if its

charge is negativenegative. However, even if

the ball is neutralneutral, the charges in the

ball can be separated by inductioninduction

(polarization), leading to a net

attraction.

a) positive

b) negative

c) neutral

d) positive or neutral

e) negative or neutral

A metal ball hangs from the ceiling

by an insulating thread. The ball is

attracted to a positive-charged rod

held near the ball. The charge of

the ball must be:

Remember the ball is a conductor!

Question 15.2a Conductors I

Follow-upFollow-up:: What happens if the What happens if the metal ballmetal ball is replaced by a is replaced by a plastic ballplastic ball??

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?

Question 15.2b Conductors IIa) 0 0

b) + –

c) – +

d) + +

e) – –

0 0

? ?

While the conductors are connected, positive positive

charge will flow from the blue to the green charge will flow from the blue to the green

ball due to polarizationball due to polarization. Once disconnected,

the charges will remain on the separate charges will remain on the separate

conductorsconductors even when the rod is removed.

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?

Question 15.2b Conductors IIa) 0 0

b) + –

c) – +

d) + +

e) – –

0 0

? ?Follow-upFollow-up:: What will happen when the What will happen when the

conductors are reconnected with a wire?conductors are reconnected with a wire?

15.3 Electric ForceThe force exerted by one charged particle on another is given by:


15.3 Electric Force

If there are multiple point charges, the force vectors must be added to get the net force.


QQ QQF1 = 3 N F2 = ?

a) 1.0 N

b) 1.5 N

c) 2.0 N

d) 3.0 N

e) 6.0 N

What is the magnitude What is the magnitude

of the force of the force FF22??

Question 15.3a Coulomb’s Law I

The force F2 must have the same magnitudesame magnitude as F1. This is

due to the fact that the form of Coulomb’s law is totally

symmetric with respect to the two charges involved. The

force of one on the other of a pair is the same as the reverseforce of one on the other of a pair is the same as the reverse.

Note that this sounds suspiciously like Newton’s 3rd law!!Note that this sounds suspiciously like Newton’s 3rd law!!

QQ QQF1 = 3 N F2 = ?

a) 1.0 N

b) 1.5 N

c) 2.0 N

d) 3.0 N

e) 6.0 N

What is the magnitude What is the magnitude

of the force of the force FF22??

Question 15.3a Coulomb’s Law I

Question 15.3b Coulomb’s Law II

a) 3/4 N

b) 3.0 N

c) 12 N

d) 16 N

e) 48 N

If we increase one charge to If we increase one charge to 44QQ, ,

what is the magnitude ofwhat is the magnitude of F F11??

44QQ QQF1 = ? F2 = ?

QQ QQF1 = 3 N F2 = ?

Question 15.3b Coulomb’s Law II

Originally we had:

F1 = k(Q)(Q)/r2 = 3 N

Now we have:

F1 = k(4Q)(Q)/r2

which is 4 times bigger4 times bigger than before.

a) 3/4 N

b) 3.0 N

c) 12 N

d) 16 N

e) 48 N

If we increase one charge to If we increase one charge to 44QQ, ,

what is the magnitude of what is the magnitude of FF11??

44QQ QQF1 = ? F2 = ?

QQ QQF1 = 3 N F2 = ?

Follow-upFollow-up:: Now what is the magnitude of Now what is the magnitude of FF22??

A proton and an electron are

held apart a distance of 1 m

and then released. As they

approach each other, what

happens to the force between

them?

a) it gets bigger

b) it gets smaller

c) it stays the same

p e

Question 15.5a Proton and Electron I

By Coulomb’s law, the force between the force between the

two charges is inversely proportional to two charges is inversely proportional to

the distance squaredthe distance squared. So, the closer they get to each other, the bigger the electric force between them gets!



and then released. As they

approach each other, what

happens to the force between

them?

a) it gets bigger

b) it gets smaller

c) it stays the same

1 22

=Q Q

F kr

p e

Question 15.5a Proton and Electron I

a) proton

b) electron

c) both the same

p e

Question 15.5b Proton and Electron II

A proton and an electron are held

apart a distance of 1 m and then

released. Which particle has the

larger acceleration at any one

moment?

The two particles feel the same forcesame force. Since F = ma, the particle with the smaller smaller

massmass will have the larger accelerationlarger acceleration.

This is the electron.This is the electron.

a) proton

b) electron

c) both the same

p e

Question 15.5b Proton and Electron II



and then released. Which

particle has the larger

acceleration at any one

moment?

1 22

=Q Q

F kr

Which of the arrows best

represents the direction

of the net force on charge

+Q due to the other two

charges?

+2Q

+4Q

+Q

a bc

d

ed

d

Question 15.6 Forces in 2D

The charge +2Q repels +Q toward the

right. The charge +4Q repels +Q

upward, but with a stronger force.

Therefore, the net force is up and to net force is up and to

the right, but mostly upthe right, but mostly up.

+2Q

+4Q

+Q

a bc

d

ed

d

+2Q

+4Q

Question 15.6 Forces in 2D

Which of the arrows best

represents the direction

of the net force on charge

+Q due to the other two

charges?

15.4 Electric Field

Definition of the electric field:

The direction of the field is the direction the force would be on a positive charge.


15.4 Electric FieldCharges create electric fields, and these fields in turn exert electric forces on other charges.

Electric field of a point charge:


a) 44EE00

b) 22EE00

c) EE00

d) 1/21/2EE00

e) 1/44EE00

You are sitting a certain distance from You are sitting a certain distance from

a point charge, and you measure an a point charge, and you measure an

electric field of electric field of EE00. If the charge is . If the charge is

doubleddoubled and your distance from the and your distance from the

charge is also charge is also doubleddoubled, what is the , what is the

electric field strength now?electric field strength now?

Question 15.7 Electric Field

Remember that the electric field is: E = kQ/r2.

Doubling the chargeDoubling the charge puts a factor of 2factor of 2 in the

numerator, but doubling the distancedoubling the distance puts a factor factor

of 4of 4 in the denominator, because it is distance

squared!! Overall, that gives us a factor of 1/2factor of 1/2.

a) 44EE00

b) 22EE00

c) EE00

d) 1/21/2EE00

e) 1/44EE00

You are sitting a certain distance from You are sitting a certain distance from

a point charge, and you measure an a point charge, and you measure an

electric field of electric field of EE00. If the charge is . If the charge is

doubleddoubled and your distance from the and your distance from the

charge is also charge is also doubleddoubled, what is the , what is the

electric field strength now?electric field strength now?

Question 15.7 Electric Field

+2 +1+1 +1d d

a)

b)

c) the same for both

Between the red and the

blue charge, which of

them experiences the

greater electric field due

to the green charge?

Question 15.8a Field and Force I

+2

+1

Both charges feel the same electric same electric

fieldfield due to the green charge because

they are at the same point in spacesame point in space!

+2 +1+1 +1d d

a)

b)


2r

QkE




greater electric field due


Question 15.8a Field and Force I

+2

+1

+2 +1+1 +1d d

a)

b)





greater electric force due


Question 15.8b Field and Force II

+2

+1

The electric field is the sameelectric field is the same for both charges,

but the forceforce on a given charge also depends

on the magnitude of that specific chargemagnitude of that specific charge.

+2 +1+1 +1d d

a)

b)





greater electric force due


qEF

Question 15.8b Field and Force II

+2

+1

15.4 Electric FieldFor multiple charges, the total electric field is found using the superposition principle:For a configuration of charges, the total, or net, electric field at any point is the vector sum of the electric fields due to the individual charges.


15.4 Electric Field

It is convenient to represent the electric field using electric field lines, or lines of force. These lines are drawn so the field is tangent to the line at every point.


15.4 Electric Field

Rules for drawing electric field lines:

1. Closer lines mean a stronger field.

2. The field is tangent to the lines at every point.

3. Field lines start on positive charges and end on negative charges.

4. The number of lines entering or leaving a charge is proportional to the magnitude of the charge.

5. Field lines never cross.© 2010 Pearson Education, Inc.

What is the electric field at What is the electric field at

the center of the square?the center of the square?

dc

b a

-2 C

-2 C

Question 15.9a Superposition I

For the upper charge, the E field vector at the center

of the square points toward that charge. For the

lower charge, the same thing is true. Then the vector

sum of these two E field vectors points to the leftpoints to the left.

What is the electric field at What is the electric field at

the center of the square?the center of the square?

dc

b a

-2 C

-2 C

Question 15.9a Superposition I

Follow-upFollow-up:: What if the lower charge were +2 C? What if the lower charge were +2 C? What if both charges were +2 C? What if both charges were +2 C?

What is the direction of

the electric field at the

position of the X ?

d

cb

a

+Q

-Q +Q

e

Question 15.9c Superposition III

The two +Q charges give a resultant E field

that is down and to the rightdown and to the right. The –Q charge

has an E field up and to the leftup and to the left, but smallersmaller

in magnitude. Therefore, the total electric total electric

field is down and to the rightfield is down and to the right.

What is the direction of

the electric field at the

position of the X ?

d

cb

a

+Q

-Q +Q

e

Question 15.9c Superposition III

Follow-upFollow-up:: What if all three charges reversed their signs? What if all three charges reversed their signs?

15.4 Electric FieldElectric field lines of a dipole:


15.4 Electric Field

Electric field lines due to very large parallel plates:


15.4 Electric Field

Electric field lines due to like charges: (a) equal charges; (b) unequal charges.


a) charges are equal and positive

b) charges are equal and negative

c) charges are equal and opposite

d) charges are equal, but sign is

undetermined

e) charges cannot be equal

Q2Q1 x

y

E

Two charges are fixed along Two charges are fixed along

the the xx axis. They produce an axis. They produce an

electric field electric field EE directed along directed along

the negative the negative yy axis at the axis at the

indicated point. Which of indicated point. Which of

the following is true?the following is true?

Question 15.10 Find the Charges

The way to get the resultant PINK vector

is to use the GREEN and BLUE vectors.

These E vectors correspond to equal equal

chargescharges (because the lengths are equal)

that are both negativeboth negative (because their

directions are toward the charges). Q2Q1 x

y

E

Two charges are fixed along Two charges are fixed along

the the x x axis. They produce an axis. They produce an

electric field electric field EE directed along directed along

the negative the negative yy axis at the axis at the

indicated point. Which of indicated point. Which of

the following is true?the following is true?

a) charges are equal and positive

b) charges are equal and negative

c) charges are equal and opposite

d) charges are equal, but sign is

undetermined

e) charges cannot be equal

Question 15.10 Find the Charges

Q

In a uniform electric field in empty In a uniform electric field in empty

space, a 4 C charge is placed and it space, a 4 C charge is placed and it

feels an electric force of 12 N. If this feels an electric force of 12 N. If this

charge is removed and a 6 C charge charge is removed and a 6 C charge

is placed at that point instead, what is placed at that point instead, what

force will it feel?force will it feel?

a) 12 N

b) 8 N

c) 24 N

d) no force

e) 18 N

Question 15.11 Uniform Electric Field

Since the 4 C charge feels a force, there must

be an electric field present, with magnitude:

E = F / q = E = F / q = 12 N12 N / / 4 C4 C = = 3 N/C3 N/C

Once the 4 C charge is replaced with a 6 C

charge, this new charge will feel a force of:

F = q E = (F = q E = (6 C6 C)()(3 N/C3 N/C) = ) = 18 N18 N

Q

a) 12 N

b) 8 N

c) 24 N

d) no force

e) 18 N

Question 15.11 Uniform Electric Field

In a uniform electric field in empty In a uniform electric field in empty

space, a 4 C charge is placed and it space, a 4 C charge is placed and it

feels an electric force of 12 N. If this feels an electric force of 12 N. If this

charge is removed and a 6 C charge charge is removed and a 6 C charge

is placed at that point instead, what is placed at that point instead, what

force will it feel?force will it feel?

Question 15.12a Electric Field Lines I

What are the signs of the

charges whose electric

fields are shown at right?

a)

b)

c)

d)

e) no way to tell

Question 15.12a Electric Field Lines I

What are the signs of the

charges whose electric

fields are shown at right?

a)

b)

c)

d)

e) no way to tell

Electric field lines originate on originate on

positive chargespositive charges and terminate terminate

on negative chargeson negative charges.

15.5 Conductors and Electric Fields

Electric charges are free to move within a conductor; therefore, there cannot be a static field within the conductor:

The electric field is zero inside a charged conductor.

Excess charges on a conductor will repel each other, and will wind up being as far apart as possible.Any excess charge on an isolated conductor resides entirely on the surface of the conductor.



There cannot be any component of the electric field parallel to the surface of a conductor; otherwise charges would move.The electric field at the surface of a charged conductor is perpendicular to the surface.



The force from neighboring charges is less when the curvature of the surface is large:

Excess charge tends to accumulate at sharp points, or locations of highest curvature, on charged

conductors. As a result, the electric field is greatest at such locations.


15.6 Gauss’s Law for Electric Fields: A Qualitative Approach

A surface, called a Gaussian surface, that completely surrounds a point charge intercepts the same number of field lines regardless of its shape. For a positive charge, the lines exit the surface; for a negative one they enter it.



If a greater amount of charge is enclosed, more field lines cross the surface.



Here, surface 1 surrounds the positive charge and has lines exiting it. Surface 2 surrounds the negative charge and has lines entering it. Surface 3 does not enclose any charge, and the same number of lines exit as enter.

Surface 4 encloses both charges; as they are equal in magnitude, the same number of lines exit the surface as enter it.© 2010 Pearson Education, Inc.


The underlying physical principle of Gauss’s law:The net number of electric field lines passing through an imaginary closed surface is proportional to the amount of net charge enclosed within that surface.

This can be used to show that excess charge on a conductor must reside on the surface.


Summary of Chapter 15

Like charges repel; unlike charges attract.

Charge is conserved.

Electrons move freely inside conductors, but not inside insulators.

Objects may be charged electrostatically by friction, conduction, or induction.

Polarization is the separation of positive and negative charge within an object.



Coulomb’s law:

The electric field, a vector, is the force per unit charge. Electric fields from multiple charges add by superposition.

Electric field lines are used to represent the electric field.

A conductor has zero electric field inside and has all excess charge on its surface.



The electric field is always perpendicular to the surface of a conductor.

The charge density and electric field are greatest on a conductor where the curvature is largest.


15_electric charge-forces-fields

Documents