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5.1. Electric Fields

This section basically embeds some of the key ideas that we need to get our heads around the key ideas of the Electricity topic. Underpinning this whole concept is the idea of electrical charge. At GCSE we were previously introduced to some of these ideas, though given that most students find these ideas tricky to visualise when first introduced, inevitably there some is misconception and confusion at the start of IB. What exactly is meant when we talk about the terms 'charge', 'current', 'voltage' or 'power'? Chapter 5.1. is mostly about defining a few key ideas which are essential for understanding what comes next.

I've broken this topic up into the following sections.

 

Charge and Fields

So let's start off by going back to basics - what exactly is charge? We understand that certain things (e.g. protons and electrons) have a positive or negative charge, but what does this really mean? Essentially, charge is a physical property of matter that causes it to experience a force when placed in an electric field. Essentially charge as we understand it (and the ideas of attraction/ repulsion) only make sense when taken in the context of their interaction with the electric field.

We remember from before that the unit of charge is the Coulomb. Electrons all have a charge of -1.6 x 10­ˉ¹⁹ C, while protons have the exact opposite charge, +1.6 x 10­ˉ¹⁹ C. Charges are able to influence other charged objects in the space around them, and this is what we mean when we discuss the idea of the electric field.

This video by Crash Course Physics is a nice little introduction to these key points.

Now take a minute to have a look at this PHET simulation. See what happens as you position different positive and negative charges in space. The resulting arrows show the Electric field around these charges. When you drag the sensor (essentially a tiny positive 'point charge') into the field, you can see the size and direction of the resulting force acting on the sensor - this is actually how electric field strength at any point is defined, that is:

Electric Field Strength is the force experienced per unit charge experienced by a small positive point charge at a point in space.

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This leads us to an equation defining electric field strength:

E = FE / q

 

This has similarities to our definition of weight, i.e. the gravitational force experienced by a mass at a point in space. Compare the following equations and note their similarities: 

Where:

E = Electric field strength (NCˉ¹)

FE = Electrostatic force (N)

q = Charge on object (C)

FE = qE

Electrostatic force experienced by a charge = charge on object x electric field strength

FG (or W) = mg

Gravitational force experienced by a mass (i.e. weight) = mass of object x gravitational field strength

This Khan Academy video nicely summarises these key points and better explains this idea of what exactly Electric fields are, and how charges can interact through empty space. 

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For a bit of fun, have a go at this 'Electric Field Hockey' game by PHET. By adding point charges you can control the movement of the hockey puck.

Electric Field Shapes

We need to know the shape of the Electric Field in certain circumstances, the most common ones being:

  • Around a simple point charge (positive or negative)

  • Between two like charges (positive or negative)

  • Between two opposite charges (called a dipole)

  • Between two parallel plates with opposite charges.

Some of these do look very similar to the magnetic field shapes you looked at for GCSE. Falstad has some nice simulations illustrating these.

Electric Fields in 2D - In this simulation you can visualise the fields in different situations. Try those examples listed above, as well as the quadrupole example. 

N.B. The default field arrows represent the force that would act on a positive test charge placed at that point. This is how we define the field shape. You can switch to Electric Field Lines in the drop down tab.

Electric Fields in 3D - You are used to seeing these drawn in 2D on the page of your book. However, it useful to remember that these fields act in 3 dimensions. Look at the above examples again and see how they compare. Switch between Particle Velocity and Electric Field Lines in the Display drop down menu.

N.B. You can take a slice through different planes (x, y or z) to obtain the 2D shapes you are more familiar with.

Now, if we imagine a uniform field between two plates with a potential difference between them. If we bring our test charge in between these plates, it will experience a force and will start to move. By considering the work done on the charge as it moves between these plates, we can derive an equation for the strength of the electric field between these plates. 

E = V/d

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Where:

E = Electric field strength (NCˉ¹)

V = Potential difference between plates (V)

d = Distance between plates (m)

(N.B. An alternative unit of Electric Field Strength therefore is Volts per metre Vmˉ¹)

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We can combine the ideas of Electric Field Strength and Projectiles in this Geogebra simulation to predict the motion of a charged particle moving between parallel plates - a good opportunity to consolidate both topics!

Try setting your initial parameters to some arbitrary values, then predict the position at which the charge will hit the plate.

 

Physics Ninja has a video walking through these problems if you are unsure how to tackle them.

Video Lessons

Resources

IB Physics
Topic 5 Notes
IB-Physics.net
Chapter 5 Summary
IB Revision Notes
Isaac Physics
Basic Concepts & Visualising Fields
Mr. G
5.1 Teaching Notes
5.1 Student Notes
Physics and Maths Tutor
Fields Notes
p1-8 are the IB relevant sections

Questions

 

Coulomb's Law

Coulomb's Law is an equation that determines the size of the force between two charged particles. As with the parallels between the equations defining electric and gravitational field strength - this equation has distinct similarities with Newton's Law of Gravitation covered in Chapter 6.2. Crash Course have another nice video introduction.

Coulomb's Law is given by the below equation. It looks a little scary at first, but it's worth spending some time familiarising yourself with it. Here, q1 and q2 are the charges on any two charged particles/ objects, while r is the separation distance between them.

F = k q1q2

           r²

 

It's worth noting that with Newton's Law of Gravitation, m1 and m2 are always positive, and gravity is always attractive. However, with Coulomb's law, if q1 and q2 are the same sign, there will be a repulsive force, whereas if they are opposite, the force will be attractive.

The 'k' in the equation is called the Coulomb constant. It is given to you in your formula book as 8.99 x 10⁹ Nm²Cˉ². It's also worth knowing where this number comes from, so for that we use the equation below (also given):

k =    1    

       4πε0

ε0 is yet another constant called the 'permittivity of free space', which can be thought of in a very over simplified way as a measure of how well free space (i.e. a vacuum) allows those field lines to pass through it. . It is given in your formula book as ε0 = 8.85 × 10ˉ¹² mˉ³ kgˉ¹ s⁴ A². I have made a short walkthrough video which talks through how to apply this equation here.

N.B.If the medium separating the charges is not a vacuum then we would need another coefficient (relative permittivity) in there to account for this (however, this is not required in the IB).

Isaac Physics have a nice multi part question giving you a bit of practice using the equation.

The Inverse Square Relationship

The law follows an inverse square relationship - i.e. that the Force is proportional to the inverse of the square of the separation distance (F ∝ 1/r²). You will see this same relationship pop up all over the place in Physics (e.g. gravitational force and light intensity from a source). The below illustration shows why this is the case, which shows light from a point source, S, spreading out - as you double the distance from r to 2r, the 'rays' from the source are spread out over an area 4 times as large, therefore are 1/4 of the intensity. From r to 3r the intensity is 1/9 as much.

Isaac Physics have a nice lesson going through the Physics and geometry behind the inverse square law.

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An IB favourite question is to find the resultant force on a charged particle near several other point charges - this involves combining Coulomb's law with a bit of geometry.  Have a go at this simulation by Geogebra - experiment by changing the charge on each point charge and the distance away, and try to predict the magnitude of the resulting force.   

Video Lessons

Resources

Questions

Note: These mixed questions contain some HL only ideas not covered in this chapter, such as Electric Potential Energy and Equipotentials - these are covered later in Chapter 10. Skip past those questions if you have not yet looked at this.

 

Electric Current

We looked at electric current throughout GCSE. Let's recap the basics.

We have an electrical current any time charge moves, and this is measured in Amps. When talking about current there are a lot of comparisons with the flow of water in rivers - in general a current is the rate of flow of something - i.e. how much moves past a point in a certain time.

Electrical current is defined as the rate of flow of charge through a point in a circuit - i.e. how many Coulombs of charge pass a point each second. Because it is defined at a certain point, ammeters are always connected in series. We'll discuss current in circuits more later on in this chapter, but let's focus on these definitions for now.

Electrical current can be summarised using the equation:

I = ΔQ

    Δt

Where:

I = Electric Current (A)

ΔQ = Charge flowing past a point (C)

Δt = time (s)

Drift Velocity

Current is caused by the movement of charges - usually this is electrons, but it could be any charged particle (e.g. ions, holes, alpha particles). The general term we give to these is charge carriers. 

We remember that conventional current is defined as being in the direction of the flow of positive charge carriers - i.e. opposite to the direction the electrons move round a circuit (as in the diagram below).

Let's now consider a small section of a conducting wire, shown in the diagram below. Conductors have free charge carriers (e.g. free electrons) that are able to freely move throughout the material (electrons in insulators are typically bound to an atom and unable to move from one atom to another). If a potential difference is applied across the ends of the conductor these charge carriers will result in a current flowing through the conductor.
 

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Where:

I = current (A)

n = charge carrier density (mˉ³)

A = cross sectional area (mˉ²)

v = drift velocity (msˉ¹)

q = charge on each carrier (C)

There is an equation which links the movement of individual charge carriers within a material to the current in Amps, given below:
 

I = nAvq

 

 

 

For a metal wire, the charge carriers are electrons. The charge carrier density is a measure of how many free electrons there are per m³ of material - and is characteristic of a particular conductor.  The drift velocity is a measure of how quickly the electrons move along the length of the wire (not the same as their average speed). Electrons in a wire are constantly moving in a random motion due to collisions with other electrons. When a potential difference is applied across the ends of the wire (ΔV), the electrons will gradually 'drift' from one end to the other, as shown by the red path below. The speed of this drift is called the drift velocity. 

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Physics Online have a nice video illustrating how the equation is derived and how it can be used.

Video Lessons

Resources

IB Physics
Topic 5 Notes
IB-Physics.net
Chapter 5 Summary
IB Revision Notes
Isaac Physics
Electric Current Concepts
Mr. G
5.1 Teaching Notes
5.1 Student Notes
Physics and Maths Tutor
Electricity Definitions
Electricity Key Points
Electricity Detailed Notes
Electricity Flashcards
A Level Resources - content slightly different

Questions

 

Potential Difference

At GCSE we were introduced to the idea of 'Voltage' - the electrical 'push' moving the charge around a circuit. However, in my experience this is one of those areas of Physics with which most students start the IB with the most misconceptions. Before diving into the electronics topic in detail it is therefore worth some time defining this idea of the Volt more thoroughly. 

 

This idea of the Volt makes much more sense for us to instead think of the voltage as the 'Potential Difference'  between two points - i.e. the difference in electric potential between two points.

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We previously looked at two plates connected to a power supply. As there is an electric field between these two plates, an electron placed at the negative plate will experience a force (upwards).

As it accelerates, there is a transfer of energy - from electric potential energy to kinetic energy.

This transfer means there is a difference in electric potential energy between the top and bottom plates i.e. a potential difference.

Now let's apply this to another example in a circuit. Let's think the electrons moving through the light bulb above your head. As the stream of electrons flows through the filament, there is an energy transfer from electrical energy to heat/ light in the bulb. Electrons entering the bulb have a high electric potential energy, while those leaving have a low electric potential energy (as it has been transferred to other types in the bulb) - as with the parallel plates, there is therefore a difference in electric potential energy across the bulb. A voltmeter placed across the terminals of the bulb will measure this potential difference, which is why it must always be connected in parallel across a component - to measure the difference in potential between two points in a circuit. 

Potential difference is therefore defined as the energy transferred per unit charge, given by the equation below:

V = W

      Q

Physics Online have a nice summary video below:

Where:

V = Potential difference (V)

W = Work done/ energy transferred (J)

Q = Charge (C)

Electromotive Force (EMF)

Batteries and cells contain a store of chemical potential energy which is transferred to electrical energy as they 'push' the charge carriers around a circuit - the size of this 'electrical push' is what we have previously called the voltage of the battery/ cell. However, it is more correct to talk about Electromotive Force, or EMF, of the power supply - typically represented with a Greek epsilon symbol, ε.

The EMF of a power supply is defined as the amount of energy supplied to each unit charge

(in contrast to the potential difference which is the energy transferred by each unit of charge).

Going back to the lightbulb example above, we can tie these ideas together. EMFs are used to describe the energy supplied to a circuit by a power supply (battery, cell etc), while potential difference is used to describe energy transferred to other types by components in the circuit (e.g. a resistor, motor, bulb).

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The Electronvolt

While we are looking at this idea of potential difference, it makes sense to introduce an important definition for a unit of energy that is extensively used in atomic physics (Chapter 7) - the electronvolt

Going back to our parallel plates example from before, now with a p.d. of 1V across them. An electron sitting at the positive plate requires energy to be supplied in order to reach the other side  to overcome the repulsive force from the negative plate. The amount of energy that needs to be supplied is how we define one electronvolt, i.e.:

One electronvolt is the energy transferred by an electron as it moves through a potential difference of 1 Volt.

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By rearranging our potential difference equation above we get:

W = QV

Here, 'V' is our potential difference of 1 V, while 'Q' is the charge on our electron, 1.6 x 10ˉ¹⁹ C (ignoring the minus sign for now). The amount of energy transferred by the electron is therefore 1.6 x 10ˉ¹⁹ J - therefore:

 

1eV = 1.6 x 10ˉ¹⁹ J

This conversion is not given in your formula book - instead you need to remember this definition and to know that the magnitude is the same as that of the elementary charge.

Video Lessons

Resources

IB Physics
Topic 5 Notes
IB-Physics.net
Chapter 5 Summary
IB Revision Notes
Isaac Physics
Electric Cells and EMF
Mr. G
5.1 Teaching Notes
5.1 Student Notes
Physics and Maths Tutor
Electricity Definitions
Electricity Key Points
Electricity Detailed Notes
Electricity Flashcards
A Level Resources - content slightly different

Questions

 

Additional Resources

IB Questions

A question by question breakdown of the IB papers by year is shown below to allow you to filter questions by topic. Hopefully you have access to many of these papers through your school system. If available, there may be some links to online sources of questions, though please be patient if the links are broken! (DrR: If you do find some broken links, please contact me through the site)

 

Questions on this topic (Section 5) are shown in pale green.

Use this grid to practice past IB questions topic by topic. You can see from the colours how similar the question topic breakdown is year by year. The more you can familiarise yourself with the IB question style the better - eventually you will come to spot those tricks and types of questions that reappear each year.