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Electric Force and Field AP Physics B

2012-11-26

Slide 3 / 86 Electric Force and Field

· Atomic Structure · Charging by Rubbing

Click on the topic to go to that section

· Charging by Conduction · Charging by Induction · Grounding · Electroscope Basics · Electric Force · Electric Field · Electric Force in 2D · Electric Field in 2D

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Atomic Structure

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Slide 5 / 86 Atomic Structure

· All matter is made up of atoms. · Each atom contains a central "nucleus". · The nucleus contains protons and neutrons, and the nucleus is considered to be at rest. · Electrons move around the nucleus in the empty space of the atom.

Slide 6 / 86 Atomic Structure

· Protons and electrons have equal and opposite electric charge. · By convention, electrons are said to have a negative charge. · Similarly, protons are said to have a positive charge. · Neutrons have no charge. · Atoms are electrically neutral...not because they contain no charge...but because they have equal numbers of protons and electrons...their total charge adds up to zero.

Slide 7 / 86 Charge

· Charge is neither created nor destroyed, it is conserved. · Opposite charges attract & like charges repel · As a result negatively charged electrons are attracted to the positive nucleus · The magnitude of charge on an electron is denoted by e. An electron is said to have a charge of

• e and a

proton a charge of +e.

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1 An atom in it's normal state has no charge. This is due to the fact that atoms

A

have only neutrons

B

have no protons

C

have no electrons

D

have an equal numbers of protons and electrons

E

are too small to measure charge

answer

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2 What symbol is used for the magnitude of charge

• n an electron or proton?

A

C

B

e

C

m

D

p

E

L

answer

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3 Which of the following is the correct force between two negative charges?

A B C D E

answer

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4 Which of the following is the correct force between two positive charges?

A B C D E

answer

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5 Which of the following is the correct force between one positive charge and one negative charge?

A B C D E

answer

Slide 13 / 86 Atomic Structure

This is NOT what an atom looks like!!! If an atom was magnified so that the nucleus was the size

• f a baseball, the atom would

be the size of our gym. And the electrons would be too small to see. Atoms are almost all empty space. Since everything, including us, is made of atoms, that means everything, including us, is mostly empty space.

Slide 14 / 86 Atomic Structure

The nuclei of atoms are much more massive than

• electrons. Each proton or neutron is 2000 times

more massive than an electron with each nucleus containing at least one proton. That's one reason that when electric charge moves it's usually the result of electrons moving, not protons. The other reason is that in solids, the nuclei are locked together so they can't move...regardless of their mass.

Slide 15 / 86 Solids

· A form of matter whose nuclei form a fixed structure. · Nuclei, and their protons, are "locked" into position. · Some electrons are bound more tightly to their atoms than other electrons. · In conductors, some electrons are free to move through the solid. · In insulators, no electrons are free to move

Slide 16 / 86 Solids

· Have strongly bound electrons which cannot move within the solid. Insulators · Some electrons move freely inside the solid. · Like charges repel, therefore the electrons spread apart as far as possible. Conductors

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Charging by Rubbing

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Slide 18 / 86 Charging by Rubbing

Rubbing two objects together · Electrons, carrying negative charge, move from one

• bject to another.

· As a result, rubbed objects each gain a net charge that is equal and opposite to the other.

without rubbing after rubbing ...rub with some fur

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6 A neutral plastic rod is rubbed by a piece of animal fur. Describe the charge on each item. A Both items will be neutral. B The fur and the rod will both have a negative net charge. C The rod will have a negative net charge and the fur will have a positive net charge. D The rod will have a positive net charge and the fur will have a negative net charge.

answer

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Charging by Conduction

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+ + + +

• Charging by Conduction

Negatively Charged (charge = -4e)

+ + + +

• Neutral Charge

(charge = 0)

• (identical

spheres very far apart) Identical spheres

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+ + + +

• Charging by Conduction

+ + + +

• Charge = -4e
• If the spheres touch, their

electrons push as far apart as they can (like charges repel)

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+ + + +

• Charging by Conduction

Negatively Charged (charge = -2e)

+ + + +

• Negatively Charged

(charge = -2e)

• (very far apart)

Once they are moved apart again, the charges cannot get back to where they came from. This results in an equal distribution

• f charge.

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7 An object with a charge of +4Q touches a neutral object. What are the new charges on each object? A no charge and +4Q B +2Q and +2Q C +4Q and +4Q D It canot be determined.

answer

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Charging by Induction

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+ + + +

• Charging by Induction

Negatively Charged

+ + + +

• Neutral
• Slide 27 / 86

+ + + +

• Charging by Induction

Negatively Charged

+ + + +

• Neutral

(but polarized)

• +

+ + +

• Neutral

(very far away)

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+ + + +

• Charging by Induction

+ + + +

• +
• -
• +

+ + -

• Negatively

Charged Positively Charged Negatively Charged Rod

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+ + + +

• Charging by Induction

+ + + +

• +
• +

+ + -

• Negatively

Charged Positively Charged Negatively Charged Rod

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+ + + +

• Charging by Induction

Negatively Charged

+ + + +

Positive Charge

• +
• -
• +

+ +

• Negatively

Charge

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8 A negatively charged sphere A is brought near a neutral sphere B without touching it. Sphere B is then touched by a

• student. What is the new charge on sphere B?

A Positive B Negative C Neutral D Cannon be determined.

answer

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Grounding

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Slide 33 / 86 Grounding

The earth is an enormous conductor. When a wire is attached between the earth and another conductor, excess electrons will flow to the earth leaving the conductor neutral. This is "grounding". Electrons flow to and from us to the earth all the time. When you touch an object with a net charge, you may get a

• shock. This is because the conductor wants to get rid of its

excess electrons. To do this, electrons flow through you to the ground.

Slide 34 / 86 Grounding

(symbol for "ground")

Electrical circuits and devices are usually grounded to protect from accumulating a net charge that could shock you. To ground an electrical device a conductor must run from the device into the ground. Plugs for many electrical devices have a third grounding pin that connects to a wire in the outlet which goes to the ground.

Grounding Pin

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9 Sphere A carries a net positive charge, and sphere B is neutral. They are placed near each other on an insulated table. Sphere B is briefly touched with a wire that is grounded. Which statement is correct? A Sphere B remains neutral. B Sphere B is now positively charged. C Sphere B is now negatively charged. D The charge on sphere B cannot be determined without additional information.

answer

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Electroscope Basics

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Slide 37 / 86 The Electroscope

The electroscope measures electrical charge. When the scope is neutral, the leaves hang down to due to their own weight. Electroscopes can be charged by conduction or induction.

Gold Leaves Conductor Insulator

• +

+ + + +

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The Electroscope

A neutral electroscope will become negatively charged when touched by a negatively charged object. Electrical charge will distribute across the electroscope and the gold leaves will repel.

• +
• +
• +

+ +

• Slide 39 / 86

(Charge = -4e)

The Electroscope

A neutral electroscope will become negatively charged when touched by a negatively charged object. Electrical charge will distribute across the electroscope and the gold leaves will repel.

• +

+ +

• +
• +

+ + + +

• (Neutrally Charged)

Slide 40 / 86 The Electroscope

• +

+ +

• +

+ +

• +
• +
• +
• +

+ +

• The bar is moved away

and there is now a negative net charge on the scope. The gold leaves repel. The leaves would repel if the experiment had been done with a bar

• f positive net charge.
• +
• +
• Slide 41 / 86

The Electroscope

A neutral electroscope can also be charged by induction. If a bar with a negative net charge is brought near the scope then the electrons in the scope will move towards the leaves and the leaves will repel. If the bar is removed, the leaves will go back to their original

• positions. This induction is temporary.

Likewise, if a positive net charge is brought near the scope, then electrons will gather at the top and the leaves will have a positive net charge. The leaves will again repel since like charge also repel.

Slide 42 / 86 The Electroscope

When the leaves of the electroscope repel, there is a charge

• present. It could be positive OR negative.

How can we determine the charge? Take an object you know to be positive or negative, place it near the top of the scope, and watch the reaction. Object's Charge is: Electroscope's Reaction: Charge on the Scope is:

Positive Leaves move apart Positive Positive Leaves move closer Negative Negative Leaves move apart Negative Negative Leaves move closer Positive

Slide 43 / 86 The Electroscope

If a neutral electroscope is connected to ground and a negatively charged bar is brought near, electrons in the scope will be repelled out of the scope to the ground. The scope will then have a positive net charge. The similar effect occurs for a bar with positive net charge except the scope will end up with a negative net charge since electrons will come from ground to the scope

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10 A positive object touches a neutral electroscope, and the leaves separate. Then a negative object is brought near the electroscope, but does not touch it. What happens to the leaves? A They separate further. B They move closer together. C They are unaffected. D Cannot be determined without additional information.

answer

Slide 45 / 86 The Electroscope

• +

+ +

• +
• +
• +

+ +

• +

(The electroscope is initially neutral) (The bar is negatively charged) What will happen when the bar is moved towards the electroscope? When the scope is grounded, negative charge will flow out of the scope to the ground. + + + +

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• +

+ +

• +
• +
• +

+ + +

The Electroscope

• +

+ +

• +

(The electroscope is now positively charged) (The bar is negatively charged)

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Electric Force

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+ + +

• +
• +
• +
• A

B Neutral Rod Conductor Stationary, Negatively Charged

If like charges repel and opposite charges attract... When A is brought towards B the electrons in A will be repelled. Electrons in A will move to the left side

• f the rod. This makes the left and right

sides of the rod have a different net charge. A positive net charge on the right side of A will cause A to move towards B. + + +

• (far apart)

Charged Objects

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If like charges repel and opposite charges attract... When A is brought towards B the electrons in A will be repelled. Electrons in A will move to the left side of the rod. This makes the left and right sides of the rod have a different net charge. A positive net charge on the right side of A will cause A to move towards B. + + +

• +
• +
• +
• A

B Neutral Rod Conductor Stationary, Negatively Charged Net Positive Charge Net Negative Charge

Charged Objects

+ + +

• Slide 50 / 86

11 What will happen when a neutral rod is brought near a negatively charged rod? A The rods will move towards each other B The rods will move away from each other C The rods will begin to spin in the counterclockwise direction D The rods will begin to spin in a clockwise direction E The rods remain at rest

answer

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12 What happens to the electrons on a neutral insulator that is brought near a negatively charged rod? A

Electrons move to the ground

B

Electrons are turned into neutrons

C

Electrons move to the side of the atoms of the insulato farthest from the rod

D

Electrons move to the side of the atoms of the insulato closest to the rod

E

Nothing happens

answer

Slide 52 / 86 Electrical Force

Newton's law of inertia says that objects at rest tend to stay at rest unless a force acts on the object. The free rod accelerated towards the free rod so there must be a force present. We call this the electrical force. In 1760, Benjamin Franklin and Joseph Priestly reasoned that the force between two charged objects must decrease as the inverse square of the distance between them: In the 1780's, Charles Coulomb showed that the electrical force was proportional to the charge (q) on each object.

Slide 53 / 86 Electrical Force

Thus, the size of the electrical force is: k = a constant that equals 9.0x10 9 Nm2/C2 |q1| = the absolute value of the net charge on one object |q2| = the absolute value of the net charge on the other object r = the distance between the objects if they are point charges, or between the centers of the objects if they are spherical.

Slide 54 / 86 Electrical Force

Charge (q) is measured in Coulombs (C). Because small amounts of charge can generate large amounts of force, charge is often measured in: milli-Coulombs (mC) = 10 -3 C micro-Coulombs (μC) = 10-6 C nano-Coulombs (nC) = 10 -9 C

Slide 55 / 86 Electrical Force

Coulomb's Law finds the size of the force. Both objects feel the same force (Newton's third law). The full solution included direction. To determine this look at the sign of both charges (like charges repel & opposite charges attract)

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13 An electric charge Q is placed at the origin. A charge q is placed at point B and the force on charge q due to charge Q is F. When q is moved to location A the force on it becomes ___ F. A F B 1/2 F C 1/4 F D 2 F E 4 F

answer

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Electric Field

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Slide 58 / 86 Slide 59 / 86 Electric Fields

Q creates the electric field. The size of charge Q and the distance to a point determine the strength of the electric field (E) at that

• point. This does not work for a uniform electric field.

Using the electric field, we can rewrite electrical force from to This equation for force works for a point charge as well as a uniform electric field. E is measured in (Newtons per Coulomb)

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14 What is the value of E if the distance from the source charge, Q, is doubled? A 4 E B 2 E C 1/2 E D 1/4 E E E

answer

Slide 61 / 86 Electric Fields

The electric field is a vector and thus has direction AND magnitude. The equation for E measures only magnitude. The direction of E is defined as the direction a positive test charge would acceleration. This equation for force works for a point charge as well as a uniform electric field.

+Q E E E E

+ + + +

Charges and Electric Fields Simulation

Slide 62 / 86 Lines of Force

A positive test charge would feel a force of repulsion A positive test charge would feel a force of attraction

Slide 63 / 86 Lines of Force

Therefore, the strength of the field decreases as distance increases. This can be see by looking at the density of the field lines.

Slide 64 / 86 Charged Metal Spheres

Calculating the electric field or force is done from the center of a charged metal sphere. When determining the distance from the sphere, measure from the center of the sphere. Within the sphere, the electric force and field are always zero.

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15 The direction of the electric field can be found by using A the direction of gravitational attraction B the direction that a positive test charge would fall C the direction that a negative test charge would fall

answer

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16 What is the direction of the electric field at the following points? A up, right , down, left B up, left, down, right C down, right, up, left D down, left, up, right

Q+

1 2 3 4

answer

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17 What is the direction of the electric field at the following points? A up, right , down, left B up, left, down, right C down, right, up, left D down, left, up, right

Q-

1 2 3 4

answer

Slide 68 / 86 The Net Electric Field

Since electric field is a vector, the net electric field at a location, due to multiple charges is calculated by adding each of the vectors together. Enet = #E Enet = E1 + E2 + E3 + ... + En where n is the total number of fields acting on a location The direction of each electric field determines the sign used.

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The Net Electric Field

Enet = #E Enet = E1 + E2 - E3

1 2 3 4 5 6 7 8 9 10

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

+Q3 +Q2 +Q1

Objective: Find the net electric field at the origin. Strategy: 1) Mark the point on the drawing for which you are solving. (here you are trying to find the E-field at the origin) 2) Draw the electric fields acting at that point. E1 E2 E3 3) Calculate E

1, E2, and E 3.

4) Combine the electric fields.

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Electric Force in 2D

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Slide 71 / 86 Electrical Force in 2-D

Until now we have only looked at the force between two charges...or three charges on a line. But if we have three or more charges that DO NOT fall on a line, we must add the forces just like we added vectors that were at angles to one another. We establish perpendicular axes that are symmetrical to the problem.

Slide 72 / 86 Electrical Force in 2-D

For example, let's calculate the force on the charge located at location C in this diagram. First, let's choose some axes for the problem.

Slide 73 / 86 Electrical Force in 2-D

Then let's draw the forces acting on the charge located at C due to the charges at A and B.

Slide 74 / 86 Electrical Force in 2-D

Then let's break those forces into components that lie on the axes. FBC FAC

Slide 75 / 86 Electrical Force in 2-D

FBCy FACy FBCx FACx If the charges are equal in magnitude, the forces will be also. We can see in this case that the x- components cancel, leaving the y-components.

Slide 76 / 86 Electrical Force in 2-D

y-axis

FBCy FACy FBCx FACx

answer Slide 77 / 86

18 Three positive charges with an equal charge of Q are located at the corners of an equilateral triangle of side r. What is the direction of the net force on charge A due to charges B and C? A B C D E

answer

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19 What is the magnitude of the net force on charge A due to two charges B and C? A B C D E

answer

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20 Four Q charges are arranged in the corner of a square as shown on the diagram. What is the direction of the net force on the test charge q placed at the center of the square? A B C D E

answer

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Electric Field in 2D

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Slide 81 / 86 The Net Electrical Field in 2-D

Until now we have only looked at the net electric field due to a single charges...or two or more charges on a line. But if we have two or more charges that DO NOT fall on a line, we must add the fields just like we added vectors that were at angles to one another. We establish perpendicular axes that are symmetrical to the problem.

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A B C D Let's determine the field on A due to charges B, C, and D. All the charges are on the corners of a square of width and length 3.0m. +90 µC +540 µC

• 90 µC

First, let's draw the electric field vectors.

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A B C D +90 µC +540 µC

• 90 µC

EB EC FD Then determine the magnitudes of the fields.

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answer

answer Then determine the components of E C. A B C D +90 µC +540 µC

• 90 µC

EB EC FD

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answer

Then determine the net electric field. A B

C D +90 µC +540 µC

• 90 µC

EB EC FD ECx ECy

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answer

A B C D +90 µC +540 µC

• 90 µC

EB EC ED ECx ECy

answer answer

Find the sum of the x-components. Find the sum of the y-components. Find the net electric fields.