Electrostatics

Learning Objectives

• The electrostatic force (Coulomb’s Law) can be either repulsive or attractive (SOL 12.a)

• The interaction of two particles can be described as: the creation of a field by one of the particles and the interaction of the field with the second particle (SOL 12.b).

• Magnitude of charge on protons and electrons are exactly the same– Protons have a positive charge– Electrons have a negative charge

• Neutral atoms contain equal numbers of protons and electrons

Insulators and ConductorsNeed to know

• Insulator: electrons are bound very tightly to the nuclei. Wood and rubber are good insulators.

• Conductor: electrons are bound very loosely and can move about freely. They are often referred to free electrons. Metals are good conductors.

• Semiconductor: very few free electrons (silicon, germanium and carbon)

Static Electricity

• You have probably experienced a charge lately (comb, dryer, carpet, car seat, …)

• An object becomes charged due to a rubbing process and is said to possess a net electric charge

• An item containing a net positive charge has lost electrons

• An item containing a net negative charge has gained electrons

Law of Conservation of Electric Charge

Need to know

The net amount of electric charge produced in any process is zero

If one object or one region of space acquires a positive charge, then an equal amount of

negative charge will be found in neighboring areas or objects

Unlike Charges Attract;Like Charges Repel

Need to know

3 Ways to Charge an ObjectNeed to know

1. Friction: Rubbing two objects together with different electron attachment. Heat generated frees electrons to join object with stronger attachment.

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are needed to see this picture.

3 Ways to Charge an ObjectNeed to know

2. Conduction: Electrons are transferred from one object to another by touching. Usually it involves moving from one electric potential to another.

John TraVOLTa Demo

3 Ways to Charge an ObjectNeed to know

3. Induction: Rod does not touch sphere. It pushes electrons out of the back side of the sphere and down the wire to ground. The ground wire is disconnected to prevent the return of the electrons from ground, then the rod is removed.

Electromagnetism

• One of the four fundamental forces of the universe (electromagnetism, gravity, weak nuclear and strong nuclear forces)

• The forces that act between atoms and molecules to hold them together are electrical forces

• Elastic, normal and contact forces (pushes and pulls) result from electric forces acting at the atomic level

Forces resulting from charges

• Charges push and pull on one another

• Closer the charge the higher the force

• The stronger the charge the higher the force

Coulomb’s LawNeed to know

The magnitude of the force between charge qA and charge qB, separated a distance d, is proportional to the magnitude of the charge and inversely proportional to the square of the distance:

F = K qAqB

d2

d

qA qB

Coulomb’s Law: Key FactsNeed to know

The charge of an electron is:-1.60 x 10-19 coulombs (C)

The charge of a proton is:1.60 x 10-19 coulombs (C)

The charge, q, is measured in coulombs. The distance, d, is measured in meters. The force, F, is measured in newtons.

The constant, K = 9.0 x 109 Nm2/C2

Problem Solving Strategy

1. Sketch the system showing all distances

2. Diagram the vectors

3. Use Coulomb’s law to find the magnitude of the force. Note: it is unnecessary to include the sign of the charges or the distance. The answer is always positive.

4. Use your diagram along with trigonometric relations to find the direction of the force

Example Problem 1

Two charges are separated by 3.0 cm. Object A has a charge of +6.0 C, while object B has a charge of +3.0 C. What is the force on object A?

Known: Unknown:

qA = +6.0 x 10-6 C FB on A = ?

qB = +3.0 x 10-6 Cd = 0.030 m

Example 1 Solution

F = K qAqB

d2

= (9.0 x 109 Nm2/C2)(6.0 x 10-6C)(3.0 x 10-6C)

(3.0 x 10-2 m)2

FB on A = 1.8 x 102 N

Example 2: Three Charges

• Given:

• Find the net force on the -2 µC charge

• Known:

-2 µC+6 µC 2 µC

6 cm 2 cm

FA on B= KqAqB

d2

= (9x109 Nm2

C2)(6x10-6 C)(2x10-6 C)(0.06 m)2

= - 30 N

FC on B= KqCqB

d2

= (9x109 Nm2

C2)(2x10-6 C)(2x10-6 C)(0.02 m)2

= + 90

FNet = FA on B + FC on B = - 30 N + 90 N = 60 N

-2 µC+6 µC 2 µC

6 cm 2 cm

Example Problem 3

A sphere with a charge 6.0 C is located near two other charged spheres. A -3.0 C is located 4.00 cm to the right and a 1.5 C sphere is located 3.00 cm directly underneath. Determine the net force on the 6.0 C sphere.

A

qA= 6 C

qc = 1.5 C

qB = -3 C

C

BdAB

dAC

FB on A

FC on AFnet

Example 3 Solution

FB on A =

FC on A =

Fnet =

=

FB on A

FC on AFnet

A

qA= 6 C

qc = 1.5 C

qB = -3 C

C

BdAB

dAC

Static Charge Generator

Electric Field Need to know

• An electric field extends outward from every charge and permeates all of space

Investigating the Electric Field

• We can quantify the strength of an electric field by measuring the force on a small positive test charge– So small that the force it exerts does not

significantly alter the distribution of the charges that create the field

aqA+

+qB

Electric Field

• An electric field, E, at any point is defined as the force, F, exerted on a tiny positive test charge at that point divided by the magnitude of the test charge:

E = F/qB

qA+

+qB

Electric Field Equation

E = F/qB

E = K qB qA/r2

qB

E = KqA/r2

qA+

+qB

Electric Field Lines

• Drawn so that they indicate the direction of the force due to the given field on a positive charge

qA+

+qB

Electric Field LinesNeed to Know

Lines indicate direction of the force due to the given field on a positive test charge

Properties of Field LinesNeed to know

1. The field lines indicate the direction of the electric field

2. The lines are drawn so that the magnitude of the electric field, E, is proportional to the number of lines crossing unit area perpendicular to the lines. The closer the lines, the stronger the field.

3. Electric field lines start on positive charges and end on negative charges

Electric Potential DifferenceNeed to know

V = Won q’ = PE: Potential difference often q’ q’ referred to as Voltage

Electric Potential Difference Units: Volt =J/C

g

BigNegativeCharge

+

+Edisplacement displacement

W = Fd = mgd W = Vq

Typical Voltages

SourceThundercloud to ground

High voltage power line

Power supply for TV tube

Auto ignition

Household outlet

Auto battery

Resting potential across nerve membrane

Potential changes on skin

(EKG)

Voltage108 V

106 V

104 V

104 V

102 V

12 V

10-1 V

10-4 V

CapacitorsNeed to Know

• A capacitor is a device that can store electric charge

• Consists of two conducting objects placed near each other but not touching

• They store charge for later use• Usage: camera flash, energy

back-up for computers and as surge protectors

Capacitors

• Consists of a pair of parallel plates of area, A, and separated by a small distance d.

• In a diagram, they are represented by the symbol:

• If a voltage is applied to a capacitor, one plate acquires a negative charge and the other an equal amount of positive charge.

CapacitorsNeed to Know

• The amount of charge acquired by each plate is proportional to the potential difference

Q = CV• Where C is constant and is called the

capacitance of the capacitor• Unit: Coulombs/Volt = Farad

– Typical capacitor range is 1pF (10-12) to 1F (10-6)

Determining Capacitance

• Constant for a given a capacitor• Depends on structure and dimensions of he

capacitor itself:

C = o A/dA = area

d = separation distance between plates

o = 8.85 x 10-12 C2/Nm2

= permittivity of free space