Topic 6: Fields and Forces

Lessons:

Syllabus Statements:

6.1.1 State Newton’s universal law of gravitation.
6.1.2 Define gravitational field strength.
6.1.3 Determine the gravitational field due to one or more point masses.
6.1.4 Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its centre.
6.1.5 Solve problems involving gravitational forces and fields.
6.2.1 State that there are two types of electric charge.
6.2.2 State and apply the law of conservation of charge.
6.2.4 State Coulomb’s law.
6.2.5 Define electric field strength.
6.2.6 Determine the electric field strength due to one or more point charges.
6.2.7 Draw the electric field patterns for different charge configurations.
6.2.8 Solve problems involving electric charges, forces and fields.
6.3.1 State that moving charges give rise to magnetic fields.
6.3.2 Draw magnetic field patterns due to currents.
6.3.3 Determine the direction of the force on a current-carrying conductor in a magnetic field.
6.3.4 Determine the direction of the force on a charge moving in a magnetic field.
6.3.5 Define the magnitude and direction of a magnetic field.
6.3.6 Solve problems involving magnetic forces, fields and currents.

Charge and its Conservation

Charge is an intrinsic property of matter (like mass). Electrons have a negative charge, protons have a positive charge and neutrons have a neutral charge. Because everything else is made up protons, electrons and neutrons they also have electrical charge.

The force between the positive charge of protons and negative charge of electrons is called electric force. Electric force is much stronger  than the gravitational force, but because most macro sized objects have equal numbers of protons and electrons, we rarely see its effects on a large scale.

Recapping what we know about the very small...

1. Atoms are composed of a positively charged nucleus, surrounded by negatively charged electrons.

2. The electrons of all atoms are identical. Each has the same quantity of negative charge and mass.

3. The nucleus is composed of protons and neutrons. Protons are about 1800 times more massive than electrons, but carry the same amount of charge (only positive). Neutrons have slightly more mass than protons, but carry no charge.

4. Atoms usually have zero net charge. ie. they have equal numbers of protons and electrons.

Questions to research:

  1. Why are the electrons not attracted by the protons into the nucleus?
  2. Why don't the oppositely charged protons in the nucleus or electrons surrounding them repel each other and fly apart.

Simple conceptual experiments to try and explain:

Materials can be charged by friction (rubbing), because this adds/ removes electrons giving them an overall charge. Then we see some interesting effects...

  1. Charging two polythene rods and observing the effect they have on each other.
  2. Charging a polythene and an acetate rod and observing the effect they have on each other.
  3. Observing the effect of a charged polythene or acetate rod on scraps of paper.

Conservation of charge

There is one underlying principle there that you have met before in a slightly different context.

Charge cannot be created or destroyed. It is an intrinsic property of all matter.

This is a cornerstone of current Physics.

Hutchings pp238, 278

Kirk and Hodgson pp127

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Gravitational Force and Field

Task:

Draw a diagram to show why someones weight on top of Everest is significantly less than at the surface of the Earth.

You can explain this effect with a Gravitational Field.

A physical field is an area in which a force occurs, a gravitational field is therefore a region of space in which an object with mass experiences a gravitational force.

When we represent fields, we draw field lines to show the direction of the force acting on a test object.

Task:

Now add field lines to the diagram you have drawn to show the Earth's gravitational field. (We call this a radial field)

 

Newton 's Law of Universal Gravitation

Any two point masses are attracted to each other with a force that is proportional to each of their masses and inversely proportional to the square of the distance between them.

There are several important points here:

  1. Point masses means that we forget about an object having a size, and consider only its mass acting at a single point (we have come across this idea before, when we considered centre of mass). This is an approximation, but a good one (read more Physics 2 pp52-53)
  2. The inverse square law - this occurs quite a lot physics and is worth going into in more detail.

The Inverse Square Law

The inverse square law considers the area over which something is spread out. For example for light eminating from a single source in all directions, its intensity is four times less when you are twice as far away from it.

Youtube clip to illustrate this with a butter gun!

Thus Newton's law of gravitation implies that the gravitational force falls off according to the inverse square law.

The mathsy bit:

Then we introduce the constant of proportionality, the universal gravitational constant, G.

And G = 6.67x10-11 Nm2kg-2

Calculation:

If the mass of the earth is 6.0x1024kg and its radius is 6400km work out the gravitational force on a 1kg mass on its surface.

 

This is the gravitational field strength on the surface of the Earth.

Gravitational field strength at a point in a gravitational field is the force exerted on a unit mass at that point.

For Earth g = 9.81 m/s2

Listen to the podcast about Newton from Bill Bryson's "A brief history of nearly everything"

Measuring g

Using light gates to measure the acceleration of a falling body:

g is related to d and t by d = ½ gt2

if we vary the distance that the mass is dropped, and get a range of times we can find a value from the gradient of a graph of t2 against d.

d (m)
t (s)
t2(s2)
     
     

g = 2/ gradient

 

Task:

Show by substitution, that the units of gravitational field strength N.kg-1 are equivilent to the units m.s-2

 

Solution:

Equating F=ma and F=-GMm/r2

If -GM/r2 = g then. F = mg

Compared with F = ma then. g must be an acceleration, a, in m/s2

Questions:

1. Calculate the gravitational force of attraction between two objects each of mass 0.1kg, separated by 1cm

2. Estimate the gravitational force of attraction between two people sitting side by side on a park bench. How does this force compare with the gravitational force exerted on them by the Earth, i.e. their weight?

3. A stone is dropped from the top of a building. It takes 1.56s to reach the ground, 12.0m below. Use these values to determine g.

Task:

Read the details of Cavendish's experiment to weigh the Earth, and then complete the worksheet.

Answer questions 9.1 and 9.2 from Hutching pp123.

Hutchings pp 120-141, Kirk and Hodgson pp142-157

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Electric Force and Field

An electric field is a region of space in which an object with charge experiences an electric force.

Task:

Draw the electric field patterns for:

A point charge A charged sphere Two point charges of the same charges. Two point charges of different charges.
  • Parallel charged plates

  • 3 point charges (2 positive and 1 negative) in the same vicinity.
  • a positive point charge in the vicinity of a negatively charged plate.

Demo:

Observe the electric field pattern set up between two charged parallel plates using the polar particles of semolena.

Coulomb's Law

The force acting between two point charges is directly proportional to each of their charges and inversely proportional to the square of the distance between them.

We use the symbol Q to denote charge.

So the equations is...

 

Applying a constant of proportionality, gives...

 

where eo = 8.85 x10 -12 C2m-2N-1 and is called the permittivity of free space. It is simply a constant of proportionality that allows us to use our conventional units for charge and force.

Given a physical significance it would denote the ease with which electric field permeates through space. It can be replaced with er, relative permittivity when the medium separating two charges isn't free space.

Task:

Read and complete the questions from the Handout: Force between point charges.

 

Electric field strength

Electric field strength at a point in an electric field is the force exerted on a unit charge at that point.

We use a positive charge of 1 coulomb as a test charge.

A field of strength E, exerts a force F on a charge +Q.

E = F / Q

Question:

What are the units of Electric field strength?

Demo:

Observe the movement of a test charge movement in different electric fields, with this applet .

Extension:

Have a go at the simulation of Millikan's Oil Drop experiment to determine the fundamental quantity of charge.

Topic 6 teaching questions on Gravitational and Electric Fields

Hutchings pp278-287 attempt questions 16.1 - 16.3, Kirk and Hodgson pp142-157

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Experiment: Drawing the electric field of two charged plates on conduting paper.

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Magnetic Force and Field

Electricity and magnetism are intrinsically linked. You cannot have one with out the other (hence the unified theory of electromagnetism).

The field shape that you will already know is that of a simple bar magnet.

But how is this related to electricity?

Basically all the atoms in the magnet are aligned so the electrons are all orbiting the same way. Each electron is moving thus you have electricity and because there is electricity there is also magnetism.

We can predict the direction of the magnetic field or current causing the field using the right hand corkscrew rule...

 

With this in mind and knowing that the earth is spinning we can determine the earth's magnetic field, and see that it looks very like that of a simple bar magnet.

 

Discuss:

  • that the magnetic and geographic poles differ

  • precession of the poles

  • elongation of the field lines (illustration)

  • inversion of the poles

Questions:

  1. A solenoid is a long coil of current carrying wire. Draw its magnetic field .

  2. Explain why what we call the north pole of the earth is in fact a magnetic south pole (think about what a navigation compass actually is).What force acts on a current carrying conductor in a magnetic field?

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Interacting Fields

We have seen that electricity produces magnetic fields, and what they look like.

Magnetic fields interact, electric fields interact, and also electric and magnetic fields interact...

We can predict the results of these interactions using Flemming's left hand rule.

Levitating aluminium foil demo.

We can measure the magnetic force of such an interaction using a current balance.

 

What factors does the magnitude of the force depend on?

  • Magnetic field strength (B) Sometimes also called magnetic flux density

  • Length of conductor in the magnetic field (l)

  • Current flowing in the wire (I)

Conveniently this gives us the equation...

F = B I l

 

NB: The units of magnetic field strength are Tesla (T).

 

This equation work well provided that the direction of the current and that of the magnetic field are perpendicular.

 

But what if they aren't?

 

You must consider the part of the B field that is perpendicular to the current.

F = B I l sin q

 

 

Tasks:

Consolidate this by doing Hutchings pp314 questions 18.1 - 18.3 and worksheet

Use the web site http://electronics.howstuffworks.com/motor1.htm to explain how a simple dc motor works. Ensure you understand what each of the components does (commutator, brushes, etc)

 

We can predict the direction and calculate the force acting on a current carrying conductor placed in a magnetic field.

The next step is to consider current as the rate of flow of charge.

This means with some simple manipulation we should also be able to predict the direction and size of forces acting on moving charges in a magnetic field.

F = B I l sin q,

 

But current, I, is the rate of flow of charge, Q/t, so...

   F = B Q/t l sin q

And this is the same as writing...

F = B Q l/t sin q

And l/t is velocity, v, so...

F = B Q v sin q

 

We often deal with electronic charge (charge associated with an electron), e, so we can also write...

F = B e v sin q

 

An important note: When we were using the Fleming's left hand rule to predict the direction of forces, etc, we were considering conventional current. We must remember that the movement of negative electrical charge is in the opposite direction to conventional current and account for this when we solve problems involving moving charges.

Task:

You now need to consolidate these ideas by doing the topic 6 questions,

Hutchings pp317 q18.4-18.

 

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Experiment: measuring Magnetic Field Strength using a Current Balance

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anrophysics 2007