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10.1. Describing Fields

Fields are everywhere. In fact, really, fields are everyTHING. Matter is caused by fluctuations in fields (at least, it does once we study Physics at uni). Kurzgesagt have a nice little introductory video to fields which is quite a nice jumping off point for the topic - particularly as it brings in some of the cool nuclear Physics ideas. 

So really, what is a field? Well, we've come across these plenty in the past: think back to drawing lines around magnets using a compass - these lines represent the area of influence of the magnet on the space around it, i.e. the magnetic field.

For IB, we mostly care about 2 types of fields, the gravitational field and the electrostatic field, both of which have some important similarities and differences. Before we dive into some extra detail here, make sure you are up to speed with the prerequisite material on Electric Fields in Section 5.1 and Gravitational Fields in Section 6.2.

 

Gravitational Fields

We’ve looked at gravitational fields before way back in Section 6.2. Here we introduced Newton’s Law of Gravitation, which follows an inverse square relationship.

Newtons Gravitation.png

Crash Course have another nice little video looking at some of the key ideas to do with gravitational fields.

The unit for gravitational field strength is Newtons per kilogram, and is defined as the gravitational force per unit mass acting at a certain point.

We can combine this with Newton’s Law of Gravitation to derive an alternative equation:

Weight and Mass.png

We also know remember the relationship between Mass (in kilograms) and Weight (in Newtons), W=mg. From this we define our gravitational field strength, i.e. the ratio between force of gravity and mass.

It is worth reinforcing the difference between these two equations at this stage – the gravitational field strength (as by definition it is the gravitational force PER UNIT MASS) depends only on the position within a field.

We have come across this idea in the past when we looked at Gravitational Potential Energy. Up until now, we normally assume a constant value for gravitational field strength (= 9.81 Nkgˉ¹ on the surface of the Earth). When distances involved in moving an object within the field are small, the field strength normally doesn’t vary much, so we can treat it is as uniform (as shown by the parallel field lines in the left picture below). However, if we are talking about moving much larger distances (such as from the surface of the planet), then the field strength will decrease (with this inverse square relationship).

g-field.png
Fields.png

Terminology is very important in this chapter, so let's start with a couple of key ideas:

  • When an object is moved further from the surface of a planet, work is done AGAINST the gravitional field (therefore it gains gravitational potential energy).

  • When an object is moved closer to the surface of a planet, work is done BY the gravitational field (therefore it loses gravitational potential energy.

  • When an object is moved along a line a constant distance from the surface of a planet, no work is done BY or AGAINST the field, so the potential energy does not change (this is called an equipotential, see below).

Finding the Neutral Point

The IB has a particular sort of question that they particularly like (particularly with the MCQs), that is related to finding the neutral point between two bodies. What this means is if we have two planets of different masses, at what point between the two is the resultant field strength equal to zero (i.e. at which point is the field strength pulling you towards each planet equal to each other).

 

I've recorded a little walkthrough video here which explains how to solve this sort of problem.  

Video Lessons

Resources

IB Physics
Topic 10 Notes
IB-Physics.net
Chapter 10 Summary
IB Revision Notes
Isaac Physics
Gravitational Fields
Mr. G
10.1 Teaching Notes
10.1 Student Notes
Physics and Maths Tutor
Fields Definitions
Fields Key Points
Fields Detailed Notes
G Fields Flashcards
A Level Resources - content slightly different

Questions

 

Electrostatic Fields

Again, we’ve come across these before, in Section 5.1.  We looked at Coulomb’s Law, another inverse square relationship with several similarities with Newton’s Law of Gravitation.

As a bit of a reminder, here it is:

Coulomb's Law.png

Take a little look at another Crash Course video summarising some of the key points.

One notable difference between the two however – the electrostatic force can be both attractive and repulsive. To measure direction of electrostatic force we use a point positive test charge as our reference.

Above we looked at our definition for gravitational field strength – that is the force per unit MASS.

Here, we have a new definition for Electric Field Strength, that is the force per unit CHARGE for a point positive test charge at certain a point in space, in Newtons per Coulomb (NCˉ¹).

E-field Strength.png

Combining these two equations gives us the following equation for electric field strength around a charged object.

E-field.png
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It’s worth reminding ourselves about the shapes of electric fields around different charges. Take a little look at this simulation by Geogebra and refresh your memory about the fields. Both Electrostatic Force and Electric Field Strength are vector quantities, as represented by the field arrows. The Electric Field Strength is the force experienced by a +1 Coulomb point charge at that point.

Finding the Resultant Electrostatic Force

The IB also does enjoy bringing in a bit of geometry to problems in this topic, getting you using your Pythagoras and trigonometry to work out resultant fields/ forces on objects. The below example looks in detail at one type of question looking at a square of charges, variations of which seems to pop up most years.

Video Lessons

Resources

IB Physics
Topic 10 Notes
IB-Physics.net
Chapter 10 Summary
IB Revision Notes
Isaac Physics
Electrostatic Fields
Vector and Scalar Fields
Mr. G
10.1 Teaching Notes
10.1 Student Notes
Physics and Maths Tutor
Fields Definitions
Fields Key Points
Fields Detailed Notes
E Fields Flashcards
A Level Resources - content slightly different

Questions

 

Equipotentials and Field Lines

To start this section off, let’s looking back at a previous example looking at two parallel plates, with a voltage between them. We have used the term potential difference to describe the voltage across a component, but what exactly does a difference in potential mean?

The example below shows a parallel plate with a potential difference of V between the plates and a seaperation distance of d metres between them. We can see from the parallel field lines between the plates there is a uniform field between the plates. What that means is if we place an electron/ point charge anywhere between those plates, it will experience the same force whether it is positioned right next to one plate or somewhere in the middle.

FieldPlates.png

The electric field strength between parallel plates is given by the equation:

E-field plates.png

Let's now look more closely at the term potential difference. In the below example, we consider the top plate having a potential of +10V, and the bottom a potential of 0 V, so a difference in potential across the plates of 10V. As we move between the plates the potential at each point decreases from +10V down to 0V.

 

With a positive test charge:

  • If it is moved towards the positive plate, work needs to be done AGAINST the field.

  • If it is moved towards the negative plate, work is done BY the field.

  • If it moves along the blue dashed lines of constant potential, NO WORK is done. These are called equipotential lines.

Equipotentials.png

These equipotential lines are very similar to contour lines on a map (as shown below left). Work must be done against the field to move higher, but moving along a contour line of constant height means no work is required. The closer together the contour lines, the steeper the surface being climbed - this is analogous to a greater field strength at that point.

If we now look at the equipotential surfaces around a positive charge (below right) we see that the equipotential lines move further apart as we get further from the charge. This is due to the field getting weaker at greater distances. We also note that the field lines are always perpendicular to the equipotential lines. 

Contour Lines.png
positive charge.png
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One of the tricky things here is visualising these three dimensional equipotential surfaces in 2D. This simulation by Geogebra allows you to move between a 2D and 3D view. Compare the equipotentials with opposite and like charged objects. 

Video Lessons

Chris Doner
Equipotentials
IB Specific
Gradepod
https://www.youtube.com/watch?v=SHykJK0qcF4
IB Specific

Resources

Questions

Cambridge University Press
Topic 10: MCQs
CUP Website Link
Freely available online
Grade Gorilla
10 (Fields) MCQs
Topic 10 (Fields) Final Quiz
Quick IB Specific Mixed MCQs
Mr. G
10.1 Formative Assessment
Topic 10 Summary Qs
IB Specific 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 10) are shown in pink.

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.