advanced higher physics unit 2 electric fields. size of charged particles powers of ten video

Advanced Higher Physics Unit 2

Electric Fields

Size of charged particles

Powers of ten video

Static ElectricityWhat do these things have in common?

Crackles when combing hair. Cling film sticking to your hands. Clothes clinging to each other

in a dryer. Getting a shock when rubbing

your feet on a carpet. Lightning.

They are all caused by static electricity.Static electricity is due to electric charge that builds up on the surface of an insulator.

The charge that has built up cannot easily flow away from the insulator, which is why it is called static electricity.

Where does static charge come from?

All materials are made of atoms, which contain electric charges.

Around the outside of an atom are electrons, which have a negative charge.The nucleus at the centre of an atom contains protons which have a positive charge.

An atom has equal amounts of negative and positive charges which cancel each other out. This means an atom has no overall charge.Electrons do not always stay attached to atoms and can sometimes be removed by rubbing.

electron (negative

charge)

proton (positive charge)

Where does static charge come from?

Static charge can build up when two materials are rubbed together, such as a plastic comb moving through hair.When this happens electrons are transferred from one material to the other:

One material ends up with more electrons, so it now has an overall negative charge.

One material ends up with fewer electrons, so it now has an overall positive charge.

Creating static charge

An insulating material can be charged by friction.

For example, if an insulator is rubbed with a cloth, it can become charged in one of two ways:

A. Electrons move from the cloth to the insulator.

B. Electrons move from the insulator to the cloth.

Charging a polythene rod

Charging a polythene rod

If an insulator made of polythene is rubbed with a cloth, electrons move from the cloth to the insulator.

The cloth is positively charged.

The insulator is negatively charged.

What charge does the cloth now have?

What charge does the polythene insulator now have?

Charging an acetate rod

Charging an acetate rod

If an insulator made of acetate is rubbed with a cloth, electrons move from the insulator to the cloth.

The cloth is negatively charged.

The insulator is positively charged.

What charge does the cloth now have?

What charge does the polythene insulator now have?

Static charge

Identifying unknown charge

If the unknown charge is brought near to a positively charged rod and it is attracted to this rod, then the unknown charge must be ________.

If the unknown charge is brought near to a positively charged rod and it is repelled by this rod, then the unknown charge must be ________.

negative

positive

If a rod has an unknown charge, how can the unknown charge be identified using a positively charged rod?

?

Identifying unknown charge

If the unknown charge is brought near to a negatively charged rod and it is attracted to this rod, then the unknown charge must be ________.

If the unknown charge is brought near to a negatively charged rod and it is repelled by this rod, then the unknown charge must be ________.

positive

negative

?

If a rod has an unknown charge, how can the unknown charge be identified using a negatively charged rod?

Inducing a temporary charge

+ - + - + -

+ - + - + -

+ - + - + -

If a negatively charged rod is brought near to a piece of paper, the paper sticks to the rod.

The paper is uncharged (equal amounts of + and -), so why does it stick to the rod?

As the negatively charged rod approaches the paper, the electrons in the paper are repelled away from the rod.

This makes one side of the paper positive and one side negative. A charge has been induced on the paper and the positive side of the paper is attracted to the negative rod.

Inducing a temporary charge

+ - + - + -

+ - + - + -

+ - + - + -

If a negatively charged rod is brought near to a piece of paper, the paper sticks to the rod.

The paper is uncharged (equal amounts of + and -), so why does it stick to the rod?

As the negatively charged rod approaches the paper, the electrons in the paper are repelled away from the rod.

This makes one side of the paper positive and one side negative. A charge has been induced on the paper and the positive side of the paper is attracted to the negative rod.

Uses of static electricityStatic electricity can be dangerous but it can also be useful, as long as it is used carefully.

Examples of uses of static electricity are:

1. ___________________

2. ___________________

3. ___________________

4. ___________________

Photocopiers

Printers

Spray painting

Pollutant removers

How a photocopier works

Electrostatic paint spray

The nozzle of the paint gun is connected to one terminal of an electrostatic generator.

The other terminal is connected to the metal panel, which is earthed.

--

--- -- -

-

Paint gun nozzle has a positive charge.

Car is negatively charged.

+

electrostatic generator

Static electricity can be used to spray a car with paint:

- -

-

- -

-

Electrostatic paint sprayThe spray gun is designed to produce tiny charged droplets of paint.

As a result the charged droplets are attracted to the car body panel. This gives a uniform coating of paint. Also, the droplets travel along the lines of force of the electrostatic field to reach hidden parts of the panel.

--

Paint gun nozzle has a positive charge.

Car is negatively charged.

electrostatic generator

--

---- -

-- -

-

- -

-+ + +

++

Danger of static electricity

Filling fuel, rollers for paper and grain shoots are situations where charge can be a problem.

Static can build up as the fuel flows along the pipe or paper rolls over rollers or grain shoots out of tubes.

This can easily lead to a spark and then an explosion.

To prevent this happening, the nozzles or rollers are made out of metal so any charge build up is conducted away.

Large petrol tankers always have earthing straps between the tanker and the storage tank to prevent the risk of sparks.

The Gold Leaf Electroscope

An electroscope can be used todetect the presence and type of charge on both metallic and non metallic objects.

Charging an electroscope

Charging an electroscope

1. Bring up a negative charge close to electroscope

Polythene rod

Charging an electroscope

2. Earth cap with finger.

Polythene rod

Charging an electroscope

3. Remove finger.

Polythene rod

Charging an electroscope

3. Remove rod.

Polythene rod

The electroscope has become positively charged.

Charging an electroscope

1. Bring up a positive charge close to electroscope

Acetate rod

Charging an electroscope

2. Earth cap with finger

Acetate rod

Charging an electroscope

3. Remove rod

Acetate rod

The electroscope has become negatively charged.

Charging two identical sphere with equal and opposite charges

1. Two initially uncharged metal spheres are touching.

Charging two identical sphere with equal and opposite charges

2. A positively charged rod is brought closed.

Charging two identical sphere with equal and opposite charges

3. Spheres are separated.

Charging two identical sphere with equal and opposite charges

4. Charged rod is removed.

The two spheres have equal and opposite charges.

Testing the sign of a charge

An electroscope is charged. For example positively.

Testing the sign of a charge

A plastic object is rubbed and brought near electroscope.

Testing the sign of a charge

If leaf rises further, the object is charged positively.

Testing the sign of a charge

If leaf goes down, the object is charged negatively.

Faraday’s Ice-Pail Experiment

1. A positively charged sphere is suspended in the can without touching the walls of the base.

2. The leaf rises.

3. Charged sphere touches the can.

4. Sphere becomes neutral but the can stays positively charged.

Coulomb’s law

Two points charges separated by a distance r exert a force oneach other- this force is called electrostatic.

Q1 Q2

r

This electrostatic force is:

•Proportional to the size of charges Q1 and Q2.

•Inversely proportional to the square of the distance r.

221

r

QQkF

With k defined as:

04

1

where

1120 1085.8 Fm

and is called the permittivity of free space

Therefore Coulomb’s Law is:2

0

21

4 r

QQF

If is positive then it is a repelling force.

If F is negative it is an attractive force.

In data

booklet.

ExampleCalculate the force on each of the 2 charges shown:

+20µC

-25µC

•Ignore sign of charge•Calculate magnitude of force first.•Work on direction of forces depending on sign of charge•Final answer should include magnitude and direction.

Electric Field

A positive charge exerts a positive (outwards) field.

A negative charge exerts a negative (inwards) field.

Two like charges

Two unlike charges

Parallel Plates

Electric Field Strength

1Q

FE

12

0

21

4 Qr

QQ

20

1

4 r

QE

The electric field strength is the force per coulomb which acharged particle experiences.Q1 generates an electric field E and Q2 experiences a force F.

Q1 Q2

r

204 r

QE

In data

booklet

With E, Electric Field Strength in NCˉ¹.

ExampleThree charges are arranged in a line as shown.

Find the electric field at point P.

•Ignore sign of charge•Calculate the electric field contribution from each charge•Work on direction of forces depending on sign of charge•Find total E by using signs•Final answer should include magnitude and direction.

Electric fields and hollow conductors

E=0

The electric field inside a conductor is zero.

The electric field is perpendicular to the surface at all points outside the conductor.

E

r

E=0 Inside: E=0

Outside: 21r

E

Faraday’s cage video

Potential

The electric potential V at a point is the work done in bringing aunit positive charge (1C) from infinity to that point.

ab

For example work is done moving test charge Qt from a to b.

Qt

Q

WV So 1 V is 1 JCˉ¹

Potential DifferenceThe potential difference V between A and B is the work done inmoving a unit positive charge from A to B.

AB

For a uniform field only: work done = force x distance

dQEQV )(

EdV

EdV

In data booklet

Therefore Electric field strength can also be measured in Vmˉ¹.

Potential due to point charges

dx

dVE

EdxdV

204 r

QE

For a non uniform field, E is a measure of potential gradient.

dxx

QdV

V r

0

204

also

dxx

QdV

204

r

V

x

QV

1

4 00

0

1

40

0 r

QV

r

QV

04

dxx

QdV

rV

2

0 0

1

4

You do not need to derive this!

Moving a positive charge from infinity requires work to be doneagainst the electric field, so the charge gains electrical potentialenergy.

We define V to be zero at infinity.

V at all point closer must be positive.

Therefore:

r

QV

04 In data booklet

Notes:

•Potential is a scalar quantity.•Potential due to several charges is the total of individual potentials.•Positive charges generate positive potentials.•Negative charges generate negative potentials.

Example

A +40µC charge is placed next to a -40µC charge as shown.

R

0.60 m 0.80 m

Determine the electrostatic potential at P and R.

Potential around a hollow conductor

rV 1

E=0

Outside asr

QV

04

Inside V= value at the edge of the conductor.This is because E=0 so no work is required to movea charge around inside the conductor.

V

r

Inside: V

Outside:rV 1

Motion in an Electric Field

QVEp

QVmv 2

2

1

AB

If a particle moves against the electric fieldit gains potential electrical energy.

If a particle moves through the electric field, its potential electrical energy istransformed into kinetic energy.

m

QVv

2

If v is 10% of c then relativistic effects need to be induced.

Not in data booklet

Example

The electric field strength between two plates is 3.6 kVmˉ¹ andthe plates separation is 25 mm.Calculate the velocity of an electron when it reaches the opposite plate.

Entering an electric field

A charged particle entering an electric field perpendicular to the field acts like a projectile in a gravitational field.

Horizontally: no force is acting on the charged particle, so it moves with a constant velocity perpendicular to the field. Vertically: there is an acceleration parallel to the field.

The acceleration is found using:

m

qE

m

Fa

Example

An electron leaves the gun of an oscilloscope. It enters a plate witha velocity of . The p.d. across the plates is 55V.

Calculate the velocity of the electron as it leaves the plates.

State if the velocity of the electron changes after leaving the plates.

16105.9 ms

Measurements

By measuring the deflection of an electron beam, find the velocityof an electron as it leaves the parallel plates.

Distance of closest approach

2

2

1

0

mvE

E

k

p

carbon nucleus

0

4 0

21

k

p

E

r

QQE

A small positive charge Q1 moving from a large distance towards a larger positive charge Q2.The initial distance is considered to be infinite.

r

At distance r, the kinetic energy has been converted into potentialenergy and so the charge stops moving. This is called the distance ofclosest approach.

change in kinetic energy = change in potential energy

r

QQmv

0

212

42

1

20

21

2 mv

QQr

Not in data booklet

ExampleA proton is travelling at towards a carbon nucleus.

Find the distance of closest approach.

16100.5 ms

Millikan’s oil drop experiment.

Millikan determined the size of the charge of an electron.He showed that there was a smallest ‘unit’ of charge or that chargeis ‘quantised’.

He did this by measuring the charge on numerous microscopiccharged oil drops.All the charges were found to come in multiples of the basic ‘unit’:2e, 3e or Ne where N is any whole number.

The charge of the electron is the smallest amount of charge detected.

Ce 19106.1

Apparatus

0V

+V

F=QE

F=mg

When the oil droplet is stationary:

d

QV EdV as

mgd

QV

V

mgdQ

As m, g and d are constant; Q is proportional to 1/V.

Measurements

V(V)

1/V (Vˉ¹)

1/V0.53

Q( )C1910