Topic 6: Fields and Topic 6: Fields and ForcesForces

Topic 6.2 Electric force and fieldTopic 6.2 Electric force and field

Electrification by FrictionElectrification by Friction

Electric charge, or `electricity', can come from batteries and generators. But some materials become charged when they are rubbed. Their charge is sometimes called electrostatic charge or `static electricity'. It causes sparks and crackles when you take off a pullover, and if you slide out of a car seat and touch the door, it may even give you a shock.

Two Types of ChargeTwo Types of Charge

Polythene and Perspex can be charged by Polythene and Perspex can be charged by rubbing them with a dry, woollen cloth.rubbing them with a dry, woollen cloth.

When two charged polythene rods are When two charged polythene rods are brought close together, they repel (try to brought close together, they repel (try to push each other apart).push each other apart).

The same thing happens with two charged The same thing happens with two charged Perspex rods.Perspex rods.

However, a charged polythene rod and a However, a charged polythene rod and a charged Perspex rod attract each other.charged Perspex rod attract each other.

Experiments like this suggest that there Experiments like this suggest that there are two different and opposite types of are two different and opposite types of electric charge.electric charge.

These are called positive (+) charge and These are called positive (+) charge and negative (‑) charge:negative (‑) charge:

Conservation of ChargeConservation of Charge

Where charges come fromWhere charges come fromEverything is made of tiny particles called Everything is made of tiny particles called

atoms.atoms.These have electric charge inside them.These have electric charge inside them.There is a central There is a central nucleus nucleus made up of made up of

protons and neutrons.protons and neutrons.Orbiting the nucleus are much lighter Orbiting the nucleus are much lighter

electronselectrons

Electrons have a negative (‑) charge. Electrons have a negative (‑) charge. Protons have an equal positive (+) Protons have an equal positive (+)

charge.charge.Neutrons have no charge.Neutrons have no charge.

Normally, atoms have equal numbers of Normally, atoms have equal numbers of electrons and protons, so the electrons and protons, so the net net (overall) (overall) charge on a material is zero.charge on a material is zero.

However, when two materials are rubbed However, when two materials are rubbed together, electrons may be transferred together, electrons may be transferred from one to the other.from one to the other.

One material ends up with more One material ends up with more electrons than normal and the other with electrons than normal and the other with less.less.

So one has a net negative charge, while So one has a net negative charge, while the other is left with a net positive charge.the other is left with a net positive charge.

Rubbing materials together does not Rubbing materials together does not make make electric charge. It just electric charge. It just separates separates charges charges that are already there.that are already there.

Charge is always conserved in any action, Charge is always conserved in any action, the distribution of charge is changed.the distribution of charge is changed.

Conductors and InsulatorsConductors and Insulators

When some materials gain charge, they When some materials gain charge, they lose it almost immediately. This is because lose it almost immediately. This is because electrons flow through them or the electrons flow through them or the surrounding material until the balance of surrounding material until the balance of negative and positive charge is restored.negative and positive charge is restored.

ConductorsConductors

Conductors Conductors are materials that let are materials that let electrons pass through them.electrons pass through them.

Metals are the best electrical conductors.Metals are the best electrical conductors.Some of their electrons are so loosely held Some of their electrons are so loosely held

to their atoms that they can pass freely to their atoms that they can pass freely between them.between them.

These free electrons also make metals These free electrons also make metals good thermal conductors.good thermal conductors.

Most non‑metals conduct charge poorly or Most non‑metals conduct charge poorly or not at all, although carbon not at all, although carbon (in the form of (in the form of graphite) graphite) is an exception.is an exception.

InsulatorsInsulators

Insulators are materials that hardly Insulators are materials that hardly conduct at all.conduct at all.

Their electrons are tightly held to atoms Their electrons are tightly held to atoms and are not free to move ‑ although they and are not free to move ‑ although they can be transferred by rubbing.can be transferred by rubbing.

Insulators are easy to charge by rubbing Insulators are easy to charge by rubbing because any electrons that get transferred because any electrons that get transferred tend to stay where they are.tend to stay where they are.

SemiconductorsSemiconductors

Semiconductors Semiconductors are `in‑between' are `in‑between' materials.materials.

They are poor conductors when cold, but They are poor conductors when cold, but much better conductors when warm.much better conductors when warm.

Electrostatic InductionElectrostatic Induction

Attraction of uncharged objectsAttraction of uncharged objectsA charged object will attract any A charged object will attract any

uncharged object close to it. For example, uncharged object close to it. For example, the charged screen of a TV will attract the charged screen of a TV will attract dust.dust.

The previous diagram shows what The previous diagram shows what happens if a positively charged rod is happens if a positively charged rod is brought near a small piece of aluminium brought near a small piece of aluminium foil.foil.

Electrons in the foil are pulled towards Electrons in the foil are pulled towards the rod, which leaves the bottom of the the rod, which leaves the bottom of the foil with a net positive charge.foil with a net positive charge.

As a result, the top of the foil is attracted As a result, the top of the foil is attracted to the rod, while the bottom is repelled.to the rod, while the bottom is repelled.

However, the attraction is stronger However, the attraction is stronger because the attracting charges are because the attracting charges are closer than the repelling ones.closer than the repelling ones.

Coulomb’s LawCoulomb’s Law

The force between two point The force between two point charges is directly proportional to charges is directly proportional to the product of the charges and the product of the charges and inversely proportional to their inversely proportional to their distance apart squared.distance apart squared.

EquationsEquations

F F q q1 1 qq22 / r / r22

Or F = k qOr F = k q1 1 qq22 / r / r22

Where k = 1/4Where k = 1/4πεπε00

εε00 is the permittivity of free spaceis the permittivity of free space Therefore Coulomb’s Law can be written asTherefore Coulomb’s Law can be written as F = qF = q1 1 qq22 / 4 / 4πεπε00rr22

Applying Coulomb’s LawApplying Coulomb’s Law

To determine the net force on a charge To determine the net force on a charge due to two or more other charges, you due to two or more other charges, you must use vector addition.must use vector addition.

Find the force and direction due to each of Find the force and direction due to each of the other charges in turn the other charges in turn

and then resolve these forces to get the and then resolve these forces to get the resultant forceresultant force

Electric FieldElectric Field

A resultant force changes motion.A resultant force changes motion. Many everyday forces are pushes or pulls Many everyday forces are pushes or pulls

between bodies in contact.between bodies in contact. In other cases forces arise between bodies that In other cases forces arise between bodies that

are separated from one another.are separated from one another. Electric, magnetic and gravitational effects Electric, magnetic and gravitational effects

involve such action‑at‑a‑distance forces and to involve such action‑at‑a‑distance forces and to deal with them physicists find the idea of a deal with them physicists find the idea of a field field of force, of force, or simply a field, useful.or simply a field, useful.

Fields of these three types have common features as Fields of these three types have common features as well as important differences.well as important differences.

An electric field is a region where an electric charge An electric field is a region where an electric charge experiences a force.experiences a force.

If a very small, positive point charge Q, the test charge, If a very small, positive point charge Q, the test charge, is placed at any point in an electric field and it is placed at any point in an electric field and it experiences a force F,experiences a force F,

then the then the field strength field strength E (also called the E‑field) at that E (also called the E‑field) at that point is defined by the equationpoint is defined by the equation

In words,the magnitude of In words,the magnitude of E E is the force is the force per unit charge and its direction is that per unit charge and its direction is that of of F F (i.e. of the force which acts on a (i.e. of the force which acts on a positive charge).positive charge).

Field strength Field strength E E is thus a vector.is thus a vector. If If F F is in newtons (N) and Q is in is in newtons (N) and Q is in

coulombs (C) then the unit of E is the coulombs (C) then the unit of E is the newton per coulomb (N newton per coulomb (N CC‑1‑1). ).

A commoner but equivalent unit is the A commoner but equivalent unit is the volt per metre (V mvolt per metre (V m‑1‑1).).

To determine the net field strength on a To determine the net field strength on a charge due to two or more other charge due to two or more other charges, use must use vector addition.charges, use must use vector addition.

Find the field strength and direction due Find the field strength and direction due to each of the other charges in turn to each of the other charges in turn

and then resolve these field strengths to and then resolve these field strengths to get the resultant field strengthget the resultant field strength

Remember that the direction of a field is Remember that the direction of a field is the direction in which a the direction in which a positive charge positive charge would move would move

Uniform Electric FieldUniform Electric Field

The field between two parallel plates can be The field between two parallel plates can be calculated bycalculated by

Field PatternsField Patterns An electric field can be represented and so visualized by An electric field can be represented and so visualized by

electric field lines.electric field lines. These are drawn so that These are drawn so that (1) the field line at a point (or the tangent to it if it is (1) the field line at a point (or the tangent to it if it is

curved) gives the direction of E at that point, i.e. the curved) gives the direction of E at that point, i.e. the direction in which a positive charge would accelerate, direction in which a positive charge would accelerate,

and (2) the number of lines per unit cross‑section area is and (2) the number of lines per unit cross‑section area is proportional to E.proportional to E.

The field line is imaginary but the field it represents is The field line is imaginary but the field it represents is real.real.

Positive Charge+