2/10 do now• Three identical metal spheres are mounted on insulating

stands. Initially, sphere A has a net charge of q and spheres B and C are uncharged. Sphere A is touched to sphere B and removed. Then sphere A is touched to sphere C and removed. In terms of q, what is the final charge on sphere A?

Due:17.2 notesQuestions from bookCastle learning 03

Assignment:Castle learning 04

Lesson 3: Electric Force

1. Charge Interactions Revisited

2. Coulomb's Law

3. Inverse Square Law

4. Newton's Laws and the Electrical Force

Objectives1. Calculate electric force using Coulomb’s law.

2. Compare electric force with gravitational force.

3. Apply the superposition principle to find the resultant force on a charge and to find the position at which the net force on a charge is zero.

• The two fundamental charge interactions are: – oppositely charged objects attract – like charged objects repel.

• These mutual interactions resulted in an electrical force between the two charged objects.

Charge Interactions are Forces

A charged PVC pipe and a paper bit interact. The electrical force on the paper bit from PVC pipe balances the weight on the paper bit. The paper remains in equilibrium.

Electric force is a non-contact force• The electrical force is a non-contact force - it exists despite

the fact that the interacting objects are not in physical contact with each other.

Two like-charged objects exert equal and opposite repulsive electrical force on each other without contact with each other.

Free body diagrams for objects A and B shown that there are three forces on each of the two objects. Both Felect and Fgrav are non-contact forces.

Force as a Vector Quantity • Being a force, the strength of the electrical interaction is

a __________________ which has both magnitude and direction.

vector quantity

• The best way to determine the direction of it is to apply the fundamental rules of charge interaction – opposites ____________.– likes ____________.

attract repel

example• An electron is located 1.0 meter from a +2.0-coulomb charge, as shown in the diagram. The electrostatic force acting on the electron is directed toward point1.  A 2.  B 3.  C 4.  D

A

B

C

D

example• Two plastic rods, A and

B, each possess a net negative charge of 1.0 × 10-3 coulomb.  The rods and a positively charged sphere are positioned as shown in the diagram.  Which vector below best represents the resultant electrostatic force on the sphere?

a b c d

Coulomb's Law

charge

distance

charge

•k is a proportionality constant known as the Coulomb's law constant. k = 8.99 x 109 N • m2 / C2. •F: force between two charges, (in Newtons)

r

q2q1

• The interaction between charged objects is a non-contact force that acts over some distance of separation. The force between two charged objects depends on three variables:– The ______________on object 1, – The ______________ on object 2, – The _________________ between them.

221

r

qqkFe

• Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.

• The force value is positive (repulsive) when q1 and q2 are of like charge - either both "+" or both "-".

• The force value is negative (attractive) when q1 and q2 are of opposite charge - one is "+" and the other is "-".

221

r

qqkFe

• Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00 meter. Determine the magnitude of the electrical force of repulsion between them.

Given:q1 = 1.00 C q2 = 1.00 Cr = 1.00 mFind: Fe =?

Fe = k • q1 • q2 / d2 Fe = (8.99 x 109 N•m2/C2) • (1.00 C) • (1.00 C) / (1.00 m)2

Fe = 9.0 x 109 NThis is an incredibly large force which compares in magnitude to the weight of more than 2000 jetliners. Objects simply do not acquire charges on the order of 1.00 Coulomb. In fact, Charge is often expressed in units of microCoulomb (µC) and nanoCoulomb (nC).

1 C = 106 μC  1 C = 109 nC

Example

• Two balloons with charges of +3.37 µC and -8.21 µC attract each other with a force of 0.0626 Newtons. Determine the separation distance between the two balloons.

Given: Find: d = ?q1 = +3.37 µC = +3.37 x 10-6 C q2 = -8.21 µC = -8.21 x 10-6 CFe = -0.0626 N (negative sign indicate attractive force)

r2 • Fe = k • q1 • q2

r2 = k • q1 • q2 / Fe

r = √(k • q1 • q2 / Fe

r = +1.99 m

Example

221

r

qqkFe

Comparing Electrical and Gravitational Forces

• Both electrical force and gravitational force are non-contact forces.

• The similarities:

Both equations have same form.

Both equations show an inverse square relationship between force and separation distance.

both equations show that the force is proportional to the product of the quantity that causes the force.

221

r

mmGFe

221

r

qqkFe

k = 8.99 x 109 N·m2/C2 G = 6.67 x 10-11 N·m2/kg2

221

r

mmGFe

221

r

qqkFe

k = 8.99 x 109 N·m2/C2 G = 6.67 x 10-11 N·m2/kg2

• The difference:Coulomb's law constant (k) is significantly greater than Newton's universal gravitation constant (G). Subsequently the force between charges – electric force - are significantly stronger than the force between masses – gravitational force. Gravitational forces are only attractive; electrical forces can be either attractive or repulsive.

example

• The diagram below shows two identical metal spheres, A and B, separated by distance d. Each sphere has mass m and possesses charge q.

•                                                   

• Which diagram best represents the electrostatic force Fe and the gravitational force Fg acting on sphere B due to sphere A?

A B C D

example

• Two protons are located one meter apart. Compared to the gravitational force of attraction between the two protons, the electrostatic force between the protons is

1.stronger and repulsive

2.weaker and repulsive

3.stronger and attractive

4.weaker and attractive

• That is, the factor by which the electrostatic force is changed is the inverse of the square of the factor by which the separation distance is changed.

• If the separation distance is doubled (increased by a factor of 2), then the electrostatic force is decreased by a factor of four (22)

• If the separation distance is tripled (increased by a factor of 3), then the electrostatic force is decreased by a factor of nine (32).

F

d

Coulomb’s Law – force and distance is inverse squared

221

r

qkqFe

example• Two charges that are 2 meters apart

repel each other with a force of 2x10-5 newton. If the distance between the charges is decreased to 1 meter, the force of repulsion will be

1. 1 x 10-5 N 2. 5 x 10-6 N 3. 8 x10-5 N 4. 4 x 10-5 N

• Electrostatic force is directly proportional to the charge of each object. So if the charge of one object is doubled, then the force will become two times greater. If the charge of each of the object is doubled, then the force will become four times greater.

Coulomb’s law – force and charge has direct relationship

221

r

qqkFe

example

• A repulsive electrostatic force of magnitude F exists between two metal spheres having identical charge q.  The distance between their two centers is r.  Which combination of changes would produce no change in the electrostatic force between the two spheres?

1.doubling q on one sphere while doubling r 2.doubling q on both spheres while doubling r 3.doubling q on one sphere while halving r 4.doubling q on both spheres while halving r

Class work

• Page 636 - Practice 17A

2/11 do now

• A typical lightning bolt has about 10.0 C of charge. How many excess electron are in a typical lightning bolt?

Homework: castle learning

Reminder:Recycle your water bottles – in the box

Recap

221

r

qqkFe

221

r

mmGFg

• The similarities:Both equations have same form. Both equations show an inverse square relationship between force and separation distance. both equations show that the force is proportional to the product of the quantity that causes the force.

• The difference:Coulomb's law constant (k) is significantly greater than Newton's universal gravitation constant (G). Subsequently the force between charges – electric force - are significantly stronger than the force between masses – gravitational force. Gravitational forces are only attractive; electrical forces can be either attractive or repulsive.

Questions • If a positively charged rod is brought near

the knob of a positively charged electroscope, the leaves of the electroscope will

1.converge, only

2.diverge, only

3.first diverge, then converge

4.first converge, then diverge

Question The diagram below represents two electrically charged identical-sized metal spheres, A and B.

If the spheres are brought into contact, which sphere will have a net gain of electrons?

1.A, only2.B, only3.both A and B4.neither A nor B

Questions • The diagram below shows two identical metal spheres, A

and B, separated by distance d. Each sphere has mass m and possesses charge q.

• Which diagram best represents the electrostatic force Fe and the gravitational force Fg acting on sphere B due to sphere A?

A B C D

Questions Which graph best represents the motion of a freely falling body near the Earth's surface?

C DA B

QuestionWhich combination of graphs above best describes free-fall motion? [Neglect air resistance.]A.A and CB.B and DC.A and DD.B and C

QuestionsTwo plastic rods, A and B, each possess a net negative charge of 1.0 × 10-3 coulomb. The rods and a positively charged sphere are positioned as shown in the diagram below.

C DA B

Which vector below best represents the resultant electrostatic force on the sphere?

Resultant force • Resultant force is the vector sum of the

individual forces on that charge.

+

+ +FA

FB

B

A

Fnet

Newton's Laws and the Electrical Force

• Electric force, like any force, is analyzed by Newton's laws of motion. The analysis usually begins with the construction of a free-body diagram. The magnitudes of the forces are then added as vectors in order to determine the resultant sum, also known as the net force. The net force can then be used to determine the acceleration of the object.

• In some instances, the goal of the analysis is not to determine the acceleration of the object. Instead, the free-body diagram is used to determine the spatial separation or charge of two objects that are at static equilibrium. In this case, the free-body diagram is combined with an understanding of vector principles in order to determine some unknown quantity.

example• A 0.90x10-4 kg balloon with a charge of -7.5 x 10-10 C is

located a distance of 0.12 m above a plastic golf tube which has a charge of -8.3 x 10-10 C. Determine the acceleration of the balloon at this instant?

free body diagram

find individual forces and Fnet & a

Fgrav = m•g = (0.90x10-4 kg)•(9.81 m/s2)

Fgrav = 8.82 x 10-4 N, down

Felect = k • q1 • q2 /r2

Felect= (8.99x109 N•m2/C2)•(-75 x 10-9 C)•(-83 x 10-9 C) / (0.12m)2

Felect = 3.89 x 10-7 N, up

Fnet = Fgrav (down) + Felect (up)

Fnet = - 8.82 x 10-4 N + 3.89 x 10-7 N

Fnet = - 8.82 x 10-4 N, down

a = Fnet / m

a = (8.82 x 10-4 N/ (0.90x10-4 kg ) a = 9.8 m/s2, down

example• Balloon A and Balloon B are charged in a like manner by

rubbing with animal fur. Each acquires 4.0 x 10-6 C. If the mass of each balloon is 1 gram, then how far below Balloon B must Balloon A be held in order to levitate Balloon B at rest? Assume the balloons act as point charges.

Felec

Fg

Fg=m•g= 0.0098 N.

Fe=m•g= 0.0098 N.

Fe = k•q1•q2 / r2

r = √ k(q1• q2) / Fe

r = 3.83 meters

Class work

• Finish practice on Coulomb's law practice and all previous practices in the packet.

Mike Kania

2/12 do now• Two charges that are 2 meters apart repel

each other with a force of 2 × 10-5 newton. If the distance between the charges is decreased to 1 meter, what is the force of repulsion?

Homework:•Castle learning•Practice Packet 4.1.1 – 4.1.3•17.3 notes•Project – levitating toy

objectives

• Finish lab

• Practice – – regents review book, pp.105-106 #1-17– All practice problems in the note packet

• Electric field

Lab 14 – Investigating Static Electricity

OBJECTIVES1.Discover the electrical properties of metallic and nonmetallic objects.2.Observe forces between charged and uncharged objects.

Requirement for each station:•Start the lab on the right side of the note book.1.Write the name of the station2.Copy the material3.Answer all questions with complete sentences.