Charge & Charge & Coulomb’s LawCoulomb’s Law

AP Physics CAP Physics C

**(1a1) Students should understand the concept of electric **(1a1) Students should understand the concept of electric charge, so they can describe the types of charge and the charge, so they can describe the types of charge and the

attraction and repulsion of charges.attraction and repulsion of charges.

• Electrons (-) and protons (+) have the same magnitude of charge.

• Atoms are electrically neutral – they have no charge. If an atom gains or loses electrons, it gains a charge and becomes an ion.

• Different elements vary widely in their ability to gain or lose electrons. – Rubber objects almost always gain a negative charge during rubbing

operations.– A glass rod rubbed with silk will gain a positive charge.

• Fundamental Law of Static Electricity Like charges repel; opposite charges attract.

• Principle of Conservation of Charge charge is not created or destroyed, merely transferred from one system to another.

**(1a2) Students should understand the concept of electric **(1a2) Students should understand the concept of electric charge, so they can describe polarization and induced charge, so they can describe polarization and induced

charges.charges.

• Conductors - usually metals. – The charge is carried through the material by the free electrons that

metals have because of their metallic bonds.• Insulators - non-metals; materials like plastic, rubber, ceramics,

etc.– These substances have their electrons tightly bound in their chemical

bonds. The charge can’t go anywhere in these substances because there’s nothing to carry the charge. The electrons are not free to move. When a charge is placed on an insulator, the charge stays where you put it.

– When a charge is placed on a conductor it will immediately spread out over the entire object

• Electrolytes are liquid solutions that can conduct electricity. The electrolyte contains ions that transfer charge.

• Charging Objects: There are two methods that can be used to charge objects:

Charging by ConductionCharging by Conduction• Charging by conduction is very simple. An object is given a

charge – we rub a rubber rod with a rabbit fur. The rod now has a negative charge. We also have a metal sphere attached to an insulated stand. We touch the sphere with the charged rod and some of the extra electrons on the rod will flow onto the sphere, giving it a negative charge.

C h arg in g by C on du ction

Charging by InductionCharging by Induction• Charging by induction is a bit more complicated. We start

out with a charged object and an uncharged object. Charge is transferred, but there is no physical contact between the two objects. There are two ways to do this.

2 3 41

1 2 3 4

Polarizing ObjectsPolarizing Objects• Polarizing is important in many of the

electrostatic phenomenon that we have played around with. For example, why did the rubber rod attract bits of paper?

• These things happen because of polarization. When you bring a charged object near an uncharged object, the uncharged object gets polarized.

• The charged balloon sticks to the wall because it polarizes the molecules in the wall and the negative charge of the balloon is attracted to the positive end of the wall’s molecules.

P olarized M olecu les

**(1b1) Students should understand Coulomb’s Law and the **(1b1) Students should understand Coulomb’s Law and the principle of superposition, so they can calculate the magnitude principle of superposition, so they can calculate the magnitude and direction of the force on a positive or negative charge due and direction of the force on a positive or negative charge due

to other specified point charges.to other specified point charges.

• The basic standard unit of charge is called a Coulomb (C).• The symbol for charge is Q however q is used as well.• One Coulomb is equal to the charge of 6.25 x 1018 electrons

or protons.• The charge of a single electron is - 1.60 x 10-19 C. The

charge of a proton is + 1.60 x 10-19 C.• The Coulomb is a large amount of charge, so it is very

common to use milli Coulombs and micro Coulombs.• 1 mC = 10-3 C• 1 C = 10-6 C• What is the charge of 1.35 x 1017 electrons?

1917 1.60 10

1.35 10 0.0216C

electrons Celectron

Coulomb’s LawCoulomb’s Law• F is the force exerted

between the two charges• q1 and q2 are the two

charges. (Note, we will actually use the absolute value of the charges - we don’t care about whether they are positive or negative.)

• r is the distance between the two charges

• is called Coulomb’s Constant. It is similar to the universal gravitational constant.

1 22

0

1

4

q qF

r

0

1

4

29

20

18.99 10

4eNm

k xC

1 2 1 22 2

e ek q q k q qF or F

r r

Coulomb ForceCoulomb Force• The force between two charged

objects can be either attractive or repulsive, depending on whether the charges are like or unlike.

• We will also assume that the charges are concentrated into a small area – point charges.

• Coulomb’s Experiment

Two point charges are 5.0 m apart. If the charges Two point charges are 5.0 m apart. If the charges are 0.020 C and 0.030 C, what is the force are 0.020 C and 0.030 C, what is the force

between them and is it attractive or repulsive?between them and is it attractive or repulsive?

291 2

2 2 20

0.020 0.03018.99 10

4 5.0

C Cq q NmF x

r C m

9 50.000216 10 2.2 10F x N x N

The force is repulsive - both charges are positive.

Gravity vs. Electromagnetic Gravity vs. Electromagnetic ForceForce

• Gravity Force Electromagnetic• Attracts attracts and

repels• inverse square law inverse square law• surround objects surround objects• cannot be shielded can be shielded• incredibly weaker enormously

stronger

**(1b2) Students should understand Coulomb’s Law and the **(1b2) Students should understand Coulomb’s Law and the principle of superposition, so they can analyze the motion of a principle of superposition, so they can analyze the motion of a particle of specified charge and mass under the influence of particle of specified charge and mass under the influence of

an electrostatic force.an electrostatic force.

• Superposition Principle: When we have more than two charges in proximity, the forces between them get more complicated. The forces, being vectors, just have to be added up. We call this the superposition principle.

• Superposition Principle The resultant force on a charge is the vector sum of the forces exerted on it by other charges.

What is the net force acting What is the net force acting on on q3q3??

+

+-

q1

q2

q3

F23F13

5.00 m

4.00 m

3.00 m

37.0 0

91 6.00 10q x C

92 2.00 10q x C

93 5.00 10q x C

What is the net force acting What is the net force acting on on q3q3??

9 9291 2

13 2 2 20

5.00 10 6.00 1018.99 10

4 5.00

x C x Cq q NmF x

r C m

9 813 10.8 10 1.08 10F x N x N

9 9291 2

23 2 2 20

2.00 10 5.00 1018.99 10

4 4.00

x C x Cq q NmF x

r C m

923 5.62 10F x N

What is the net force What is the net force acting on acting on q3q3??

13 23cosxF F F

8 91.08 10 cos37.0 5.62 10xF x N x N

9 9 98.63 10 5.62 10 3.01 10xF x N x N x N

13 sinyF F 8 91.08 10 sin37.0 6.50 10o

yF x N x N

cos

FF

Fs in F

What is the net force What is the net force acting on acting on q3q3??

2 22 2 9 9 18 26.50 10 3.01 10 51.31 10y xF F F x N x N x N

97.16 10F x N

1tan Y

X

F

F

91

9

6.50 10tan

3.01 10

x N

x N

65.2

Now we can find the direction or the resultant force:

with the x axis