Electric Charge and Electric Field

Ch 16

Static Electicity

• Electricity comes from the Greek work elektron which means “amber”.

• Static Electricity = amber effect

• Ex: a glass rod or plastic ruler rubbed with a cloth attracts tiny pieces of paper

Other Examples

• Clothes out of clothes dryer

• Combing your hair

• Shock when you touch a metal doorknob

Electric Charge

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

• There are two types of electric charge, positive and negative.

• These denominations are to be taken algebraically- plus and minus sign

Unlike Charges attract; Like Charges repel

Law of Conservation of Charge

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

• Firmly established as those for energy and momentum

• Benjamin Franklin (1706-1790)• Whenever a certain amount of charge is

produced on one body in a process, an equal amount of the opposite type of charge is produced on another body

Electric Charge in an atom

• Electricity starts inside the atom itself

• Positively charged nucleus surrounded by negatively charged electrons

• Ion: atom with a positive or negative charge

• Charge can leak off onto water molecules in the air

Water molecule is polar

• Why is it hard to perform any static electricity demos or experiments on humid or rainy days?

• On dry days, the air contains fewer water molecules to allow leakage. On humid, it is difficult to make any object hold its charge for long.

Insulators and Conductors

• Conductors: materials where some of the electrons are bound very loosely and can move about freely within the material (free electrons)

Ex: metals

• Insulators: materials where the electrons are bound very tightly to the nuclei

Ex: wood, rubber

Semiconductors

• Semiconductors: materials that fall into an intermediate category

Ex: silicon, germanium, carbon

• Conductors: a lot of free electrons

• Semiconductors: very few free elctrons

• Insulators: almost no free electrons

Methods of Charging

• By Conduction: or by contact. The two objects end up with the same sign of charge

• By Induction: a charged object is brought close to a neutral object but does not touch.

Charging by Induction

• Inducing a charge on an object connected to the ground by a metal wire (“grounded”), the object will acquire a charge opposite to the charged object.

• Earth is so large and can conduct, can easily accept or give up electrons. It acts like a reservoir for charge.

Electroscope

• Electroscope: is a device that can be used for detecting charge.

• The greater the amount of charge, the greater the separation of the leaves

Electrostatic Conduction

• Electroscope charged by conduction

Electrostatic Induction

• Electroscope charged by induction:

Sign of charged object

• How can you use an electroscope to determine the sign of a given charge?

• Bring a charged object of known charge close to a charged electroscope with an unknown charge and observe the separation of the leaves

Coulomb’s Law

• An electric charge exerts a force on other electric charges. What factors affect the magnitude of this force?

• charges• distance between charges• F = k Q1 Q2

r2

Direction of the electric force

The direction of the electric force is always along the line joining the two objects and will depend on whether the charges have the same sign or opposite signs.

Coulomb’s Law

• It gives the force between two points charges, Q1 and Q2, a distance r apart

• k : the proportionality constant• k = 8.988 x 109 N. m2/C2

• Unit for charge: the coulomb • 1 C is a very large charge. Charges produced by

rubbing ordinary objects are typically around a microcoulomb ( 1 µC = 10-6 C)

Elementary Charge

• Charge of the electron, the elementary charge, is the smallest charge

• 1 e = 1.602 x 10-19 C

• Electron : -e

• Proton: +e

• Electric charge is quantized, existing only in discrete amounts: 1e, 2e, 3e, etc

Coulomb’s Law in terms of ε0

• The constant k is often written in terms of another constant,ε0, called permittivity of free space.

• k = 1

4Лε0

• Other fundamental equations are simpler in terms of ε0 rather than k

Coulomb’s Law

• Apply to objects whose size is much smaller than the distance between them

• Point charges: spatial size negligible compared to other distances

• Charges are at rest (electrostatic)

• It gives the force on a charge due to only one other charge

Solving Problems involving Coulomb’s Law

• Ignore the signs of the charges

• Determine direction based on whether the force is attractive or repulsive

• If several charges are present, the net force on any of them will be the vector sum of the forces due to each of the others

Con’t

• When dealing with several charges, it is often helpful to use subscripts on each of the forces involved

• The first subscript refers to the particle on which the force acts; the second refers to the particle that exerts the force

• Ex: F31 means the force exerted on particle 3 by particle 1.

• Very important to draw the free body diagram for each body showing all the forces acting on that body

Gravitational x Electric Force

• Both inverse square laws (F ˜ 1/r2)

• Mass for gravity, charge for electricity

• Gravity always attractive

• Electric force can be either attractive or repulsive

Electric Field

• The idea of forces acting at a distance was a difficult one for early thinkers

• The idea of field was introduced by Michael Faraday (1791-1867)

• Electric Field: extends outward from every charge and permeates all of space

Electric Field

• We can investigate the electric field surrounding a charge or group of charges by measuring the force on a small positive test charge

• Test charge: a charge so small that the force it exerts does not significantly alter the distribution of the charges that create the field being measured

Definition of Electric Field

• The electric field is defined in terms of the force on such positive test charge

• E = F q“The electric field at any point in space is a

vector whose direction is the direction of the force on a positive test charge at that point, and whose magnitude is the force per unit charge.”

Direction of Electric Field

• The electric field due to a positive charge points away from the charge

• The electric field due to a negative charge points toward that charge

• If q is positive F and E will point in the same direction. If q is negative, F and E point in opposite directions

Electric Field due to one point charge

• E = k q Q/ r2

q

= k Q

r2

• In terms of ε0

• E = 1 Q

4Лε0 r2

• Notice that E is independent of q, that is, it depends only on the charge Q which produces the field, and not on the value of the test charge q

Superposition principle for electric fields

• If the field is due to more than one charge, the individual fields, E1, E2,etc, due to each charge are added vectorially to get the total field at any point

• E = E1 + E2 + …..

Problem Solving Electrostatic

1. Draw a careful diagram

2. Apply Coulomb’s law to get the magnitude of the forces or the electric field

3. Determine the direction of each force or electric field physically (like charges repel, unlike attract)

4. Add vectorially forces or fields to get resultant

5. Use symmetry (geometry) whenever possible

Field Lines

• In order to visualize the electric field, we draw a series of lines to indicate the direction of the electric field at various points in space. These electric field lines (sometimes called lines of force) are drawn so that they indicate the direction of the force due to the given field on a positive test charge.

Fild Lines

• Number of lines starting on a positive charge, or ending on a negative charge, is proportional to the magnitude of the charge

• The closer the lines are together, the stronger the electric field in that region

Field Lines

• The direction of the field at any point is directed tangentially

Field Lines

• For unequal charges, for example +2Q and -Q, twice as many lines leave + 2Q as there are lines entering -Q

Field Lines

• Field lines between two opposite charged parallel plates

• Field lines are parallel and equally spaced except near the edges

• Electric field has the same magnitude, constant, in the central region

Properties of Field Lines

1. They indicate the direction of the electric field (tangent to the field line at any point)

2. The magnitude of the electric field is proportional to the number of lines crossing unit are perpendicular to the lines (closer the lines, stronger the field)

3. They start on + charges and end on – charges (the # is proportional to the magnitude of the charge)

Electric Fields and Conductors

• The electric field inside a good conductor is zero in the static situation

• If there were an electric field within the conductor, there would be a force on its free electrons, the electrons would move (not static situation)

• Main consequence: Any net charge on a good conductor distributes itself on the surface.

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

• If there were a component parallel to the surface, electrons would move along the surface in response to that force (not static situation)

Why are you safer inside your car during a thunderstorm?

• The electric field inside is zero

Shielding and safety in a storm

• Conducting metal box is often used for shielding delicate instruments and electronics circuits from unwanted external electric fields

• A relatively safe place to be during a lightning storm is inside a car, surrounded by metal