Imagine you have been asked to write a report with the title “How Maxwell unified the physics of electricity, magnetism, and light”. The report should be appropriate for a student preparing to start studying S217. You need to

Question  1 – 10 marks

This question is designed to assess your reflection on your learning, your communication skills and your engagement with interactive Quiz 4, covering Units 10, 11, 12 and 13.

(a) To demonstrate your engagement with Quiz 4, paste into your TMA answers a screenshot of either the summary page showing your performance on Quiz 4 or the screen that gives your overall score for this quiz. It does not matter what score you obtained; we are interested in your engagement with the quiz. Remember also that you may attempt the quiz questions as often as you wish, and each question has multiple

variants that will be presented to you in turn, each time you try it. [2]

(b) In a few sentences, describe one thing that you learnt from answering the questions in Quiz 4 that improved your understanding of electrical circuits or magnetic fields.Your answer should be clearly explained and

you should not need to write more than 100 words to answer part (b). [4] (Even if you scored full marks on the quiz the first time you tried it,

hopefully you learnt something of relevance in completing it. If you feel

that this was not the case, your statement to this effect should be supported by your screenshot in part (a).)

(c) (i) Name one skill that was identified in the feedback you received from your tutor on TMA 02 or TMA 03 as needing further development, and explain what you have done to develop this skill.

(ii) Explain how you expect that your answers to TMA 04 will have improved as a result of the development of the skill identified in

part (c)(i). [4]

Your answers should be clearly explained and you should not need to write more than 100 words in total to answer part (c).

(If your tutor did not identify any skills that you needed to develop, you should base your answers on a skill, or skills, that you have identified for development yourself.

Question  2 – 30 marks

This question is designed to test your ability to analyse and interpret experimental data in the context of the magnetic field produced by a current passing through a coil (or two coils) of wire (Unit 11).

The question provides data that was acquired using the Magnetic field of Short Coils interactive screen experiment (ISE) in Unit 11, Section 3.3, Activity 1. Although it is not necessary to acquire any data yourself, you may find it useful to explore the ISE while you work through the question. This might help you to visualise the fields produced in the situations described below.

A student uses the ISE to set up a single coil that carries a current of

I = 5.00 A. The situation is illustrated in Figure 1 below.

r

R

x

observer

Figure 1 The single coil used in Question 2 parts (a), (b) and (c). The current direction in the coil is anticlockwise, as viewed by the observer.

(a) Based on the information in Figure 1, deduce the direction of the magnetic field at position (x = 0, r = 0). Explain your reasoning

carefully with the aid of a sketch. [4]

(The ISE does not allow you to specify the direction of the current in the coil, so it is not very helpful for part (a).)

(b) The student sets the coil radius at R = 22.5 cm, the number of turns at N = 90.0, and keeps the current at I = 5.00 A. They then measure the x-component of the magnetic field (B_x) at various (x, r) coordinates. Considering the symmetry of the arrangement, they decide that it is not necessary to take measurements at negative x coordinates. The student records their data in Tables 1 and 2.

Table 1 Values for the x-component of the magnetic field B_x in µT at various x coordinates with r = 0. R = 22.5 cm, N = 90.0 turns and I = 5.00 A. Table 1 is included here for interest, but you do not need to use values from this table until part (d).

Table 2 Values for the x-component of the magnetic field B_x in µT at various

r coordinates with x = 0. R = 22.5 cm, N = 90.0 turns and I = 5.00 A.

(i) Use the data in Table 2 to plot a graph of B_x against r when x = 0.

You may plot your graph by hand or using a computer. [5]

(ii) Briefly explain why drawing a smooth curve through all your data points would not represent B_x accurately between (x = 0, r = 20.0 cm)

and (x = 0, r = 25.0 cm). [2]

(c) The student then decides to measure B_x at the centre of the coil as a function of the coil radius R. I and N are kept at 5.00 A and 90.0 turns, respectively. The student records their data in Table 3.

Table 3 Values for the x-component of the magnetic field at position (0, 0) for various values of R.

(i) Use the data in Table 3 to produce a table of ln(B_x(0, 0)/µT) against ln(R/cm). [2]

(ii) Use the data in your table from part (c)(i) to plot a graph. You may plot your graph by hand or using a computer. Draw a line of best fit

through your data points. [3]

(iii) By analysing your line of best fit from part (ii), deduce the relationship

between B_x(0, 0) and R. Show your working. [3]

(d) Now consider two coils separated by a distance S. Each coil is the same as the coil in part (b) (R = 22.5 cm, N = 90.0, and I = 5.00 A). The arrangement is illustrated in Figure 2. The coils are centred on the

x-axis and the origin of the coordinate system is midway between the two coils.

r

R

x

observer 

Figure 2 The arrangement of the two coils as used in Question 2(d). The current direction in each coil is anticlockwise, as viewed by the observer.

(i) For S = 20.0 cm, deduce the x-component of the total magnetic field B_x as a function of x when r = 0. You should make use of the student’s data from Table 1, show your working, and state any assumptions that

you have made. Present your deduced values in a table. [7]

Hint: Table 1 allows you to deduce the field produced by each individual coil at various (x, r = 0) coordinates, but keep in mind that neither of the coils are located at x = 0 in this part of the question. You will need to think carefully about how to convert the x values in Table 1 to the x values that you need here. Once you have carried out the appropriate conversions, you will be able to work out the total field produced by both coils at a given (x, r = 0) position shown in Figure 2. If in doubt, you can set up a pair of coils in the ISE with appropriate parameters, and then check if your deduced B_x(x, r = 0) values agree with your measurements from the ISE.

(ii) Plot the data from your table on a graph. Your B_x(x, r = 0)-axis range should be 1,600 – 2,000 µT to aid your comparison in part (d)(iii). You

may plot your graph by hand or using a computer. [2]

(iii) Figure 3 shows deduced values of B_x(x, r = 0) between the coils when

S = 22.5 cm (a Helmholtz pair where S = R). Compare your graph from part (d)(ii) with Figure 3. Briefly comment on what this comparison

tells you about using two coils to set up a uniform magnetic field. [2]

2000

1950

1900

1850

1800

1750

1700

1650

1600

−12.5 −10 −7.5 −5 −2.5 0 2.5 5 7.5 10 12.5

x / cm

Figure 3 The x-component of the total magnetic field B_x(x, r = 0) between the coils in a Helmholtz pair (S = R = 22.5 cm). For use in Question 2(d)(iii).

Question  3 – 30 marks

This question is designed to test your ability to evaluate sources of information (Unit 6), in the context of the topic of Maxwell’s equations of electromagnetism (Unit 12). It will also test your ability to communicate physical principles.

Imagine you have been asked to write a report with the title “How Maxwell unified the physics of electricity, magnetism, and light”. The report should be appropriate for a student preparing to start studying S217. You need to evaluate two source materials for your report.

Watch the video (1) and read the article (2) below. A transcript is available for the video. The article includes a link to an animation video with no speech or captions. The article also provides a link to a paper that provides extra information about the animation video, but that link is broken.

1. Glasgow Science Centre (2015) James Clerk Maxwell - What’s the go o’ that?. 1 September. Available at: https://www.open.ac.uk/libraryservices/resource/video:      154884&f=27913 (Accessed: 11 July 2024).
2. J. Butterworth (2015), ‘Maxwell’s equations: 150 years of light’, The Guardian, 23 November. Available at: https://www.open.ac.uk/libraryservices/resource/   newspaperarticle:154890&f=27913 (Accessed: 11 July 2024).

(a) Use the PROMPT criteria to evaluate the video and the article as sources of information relating to how Maxwell unified the physics of electricity, magnetism and light.

You should present your PROMPT evaluation as a table using the template provided on the S217 Assessment page. For each article, give a few short statements to address each of the PROMPT criteria (bullet points are sufficient), except for the Methods criterion.

The Methods section has already been completed in the template to give you an indication of the sort of statements that are required. For each of the other five PROMPT criteria, four marks are available for your

statements. [20]

(b) Using the video and the article above as source material, as well as S217 Unit 12, Chapter 4, write between 150 and 300 words for your report to explain:

How electromagnetic waves are a consequence of the physics of electric and magnetic fields described by Maxwell’s equations.

What led Maxwell to postulate that visible light is an electromagnetic wave.

Your explanation should be written in prose (one or two paragraphs without bullet points) and in your own words. Use concise terms, without mathematics. You should be able to answer part (b) within 150-300 words and you will lose one mark for this question if your answer is more than 300 words in length. (You will not lose marks explicitly for an answer that is shorter than 150 words, but this may be an indicator that you have not given sufficient information to obtain full marks.) You should give a word count at the end of your answer e.g. [223 words].

Keep in mind that the video and the article above are pitched at a more general audience than your report. This is why it is important for you to draw on your understanding from S217 as well as from the two

popular science sources when you answer this part of the question. [10]

Question  4 – 30 marks

This question is designed to test your ability to solve physics problems in the context of special relativity (Unit 13) using the problem-solving format outlined in Unit 1.

A space dust probe travels past Earth at a constant speed of 0.500 c in Earth’s frame of reference. Its passage occurs at 0 s in Earth’s frame and in the space dust probe’s frame.

Unfortunately, the space dust probe’s solar panel is faulty. After collecting and analysing lots of interesting dust, the space dust probe does not have enough energy to transmit the data in a signal that can be detected at Earth.

A rapid probe travels at a constant speed of 0.800 c in Earth’s frame. It passes Earth at 1.00 × 10⁸ s in Earth’s frame. At this instant, a signal is sent from Earth instructing the rapid probe to retrieve the data when it reaches the space dust probe.

At the instant that the rapid probe passes the space dust probe, the space dust probe emits a weak signal containing the data.

Figure 4 illustrates the positions of the two probes at a time t in Earth’s frame. Both probes travel in the x -direction throughout their journeys.

y

Earth

rapid probe

x

space dust probe

Figure 4 For use in Question 4

A light-second (symbol c s) is defined as the distance travelled by light in one second. Keep distances in light-seconds and speeds as multiples of c in your calculations.

(a) Preparation

The text above describes three distinct events: the space dust probe passes Earth, the rapid probe passes Earth, and the rapid probe passes the space dust probe.

(i) Use appropriate symbols to write down the (position, time) coordinates of each event in the three frames mentioned in the question. Define each set of coordinates and each symbol clearly,

and do not substitute in any values yet. [5]

(ii) Using standard configuration, draw a labelled diagram showing the three frames at the event where the rapid probe passes the space dust probe. Label the event in each frame using the relevant (position, time) coordinates from your answer to part (i).

Your diagram can be based on Figure 4 and it should show the

spatial axes of all three frames. [6]

(b) Working

(i) In Earth’s frame, calculate the (position, time) coordinates of the

event where the rapid probe passes the space dust probe. [5]

(ii) Now apply the appropriate Lorentz transformations to calculate the (position, time) coordinates of the same event in the space dust

probe’s frame. [6]

(iii) Use the time coordinate that you calculated for part (b)(ii) to calculate the position of Earth in the space dust probe’s frame at

the instant that the rapid probe passes the space dust probe. [2]

(a) Checking

(i) Does the position coordinate that you calculated using a Lorentz transformation in part (b)(ii) match what you expect? Explain

your answer. [1]

(ii) Show that your calculated time for part (b)(ii) agrees with the time predicted using the time dilation equation. [3]

(iii) Explain one other check that you have carried out on your part (b) answers. [2]