## The worst circuit in the world (part 2)

What is the worst circuit in the world? Many teachers think it is the one below.

This is the circuit that AQA (2018: 47) strongly suggest should be used to capture the data for plotting IV characteristics (aka current against potential difference graphs) for a fixed resistor, a filament lamp and a diode. The reasons why it is ‘the worst circuit in world’ were outlined in part one; and also some reasons why, nonetheless, schools teaching the 2016 AQA GCSE Physics / Combined Science specifications should (arguably) continue to use it.

The procedure outlined isn’t ‘perfect’ but works well using the equipment we have available and enables students to capture (and plot using a FREE Excel spreadsheet!) the data with only minor troubleshooting from the teacher.

### Step the first: ‘These are the graphs you’re looking for.’

I find this required practical runs more smoothly if students have some awareness of what kind of graphs they are looking for. So, to borrow a phrase, I usually just tell ’em.

You can access an unannotated version of the slides on Google Jamboard and pdf below.

### Step the second: capture the data for the fixed resistor

It is a continual source of amazement to me that students seem to find a photograph of a circuit easier to interpret than a nice, clean, minimalist circuit diagram, so for an easier life I present both.

You can, if you have access to ICT, get the students to plot their results ‘live’ on an Excel spreadsheet (link below). I think this is excellent for helping to manage the cognitive demand on our students (as I have argued before here). Please note that I have not used the automated ‘line of best fit’ tools available on Excel as I think it is important for students to practice drawing lines of best fit — including, especially, curved lines of best fit (sorry, Maths teachers, in science there are such things as curved lines!)

### Step the second: capture the data for the filament lamp

In this circuit, we replaced the previous 0-16 ohm variable resistor with a 0 – 1000 ohm variable resistor paired with 2.5 V, 0.2 A filament lamp because the bulb has a resistance of about 60 ohms when run at 2.5 V and so the 0-16 ohm variable resistor is often ineffective. We allowed a maximum potential difference of just over 3.0 V to ‘over run’ the bulb so as to be sure of obtaining the ‘flattening’ of the graph. The method calls for very small adjustments of the variable resistor to obtain noticeable changes of brightness of the bulb. Note that the cells used in the photograph had seen many years of service with our physics department(!) and so were fairly depleted such that three of them were needed to produce a measly three volts; you would likely only need two ‘fresher’, ‘newer’ cells to achieve the same.

### Resources

And, by popular request, a copy of the PowerPoint below (although, trust me, I think Google Jamboard is superior when using ‘live’ in front of a class)

REFERENCES

## ‘Isn’t it ionic?’: Showing the circular motion of charged particles in magnetic fields in the school laboratory

Charged particles which are stationary within a magnetic field do not experience a magnetic force; however, charged particles which are moving within a magnetic field most definitely do. And, what is more, this magnetic force or Lorentz force always makes them move on circular paths or semicircular paths. (Note: for simplicity we’re only going to look at particles whose velocity is perpendicular to the magnetic field lines in this post.) The direction of the Lorentz force can be predicted using Fleming’s Left Hand Rule.

An understanding of this type of interaction is essential for A-level Physics as far the physics of particle accelerators and cyclotrons are concerned. It is, of course, desirable to be able to demonstrate this to our students in the school laboratory. Your school may be lucky enough to own an electron beam tube and a pair of Helmholtz coils that is the usual way of displaying this phenomenon.

Bob Worley (@UncleBo80053383) recently made me aware of a low cost, microscale chemistry demonstration that I believe shows this phenomenon to good effect. If the electrolysis of sodium sulfate is carried out over a strong neodymium magnet then the interaction between the electric and magnetic fields creates clear patterns of circulation that are consistent with the directions predicted by the movement of the ions within the electric field produced by the electrodes and the Fleming’s Left Hand Rule force on the ions produced by the external magnetic field.

Please note that in the following post, any errors, omissions or misconceptions are my own (especially with the chemistry ‘bits’).

### Why do charged particles move on circular paths when they travel through magnetic fields?

In the diagram below, the green area represents a region of uniform magnetic flux density B. The field lines are directed into the plane of the diagram. Let’s consider an electron (1) fired at a horizontal velocity v from an electron gun as shown.

Fleming’s Left Hand Rule predicts that an upward force F will be produced on the electron. (Remember that the current in FLHR is conventional current so the ‘I’ finger should be pointed in the opposite direction to v because electron have a negative charge!) This will alter the direction of v so that the electron moves to position (2). Note that the magnitude of v is unaltered since F is acting at right angle to it. In position (2), FLHR again predicts a force F will act on the moving electron, and this force will again be at right angles to v resulting in the electron moving to position (3). Since the magnitude of v remains unaltered and F is always perpendicular to it, this means that F acts as a centripetal force which means that the electron travels at uniform speed around a circular orbit of radius r.

It can be shown that r = mv/Bq where m is the mass of the particle and q is its charge.

### Setting up the electrolysis of sodium sulfate in a magnetic field

The equipment is set up as shown in the diagram above. This can be seen from 0:00 to 0:10 seconds on the video. The magnetic field produced by the magnet can be thought of as a uniform vertical field through the volume of the drop.

Next, a few drops of red litmus are added. Since the sodium sulfate solution is neutral, the red litmus does not change colour.

At 0:15 seconds, the electrodes are introduced to the solution. Note that the anode is on the left and the cathode is on the right.

### Observing the circular motion of charged particles in a magnetic field (part 1)

Almost immediately, we see indicator change colour next to the cathode. Since sodium sulfate is a salt produced using a reactive metal and an acid containing oxygen, the electrolysis will result in hydrogen gas at the cathode and oxygen at the anode. In other words, water will be electrolysed.

At the cathode, water molecules will be reduced to form H2 and OH.

It is the OH ions that produce the colour change to purple.

From 0:23 to 0:27 we can clearly an anticlockwise circulation pattern in the purple coloured region.

This can be explained by considering the forces on an OH ion as shown on the diagram below.

As soon as it is created, the OH ion will be repelled away from the cathode along an electric field line (blue dotted lines). This means that it will be moving at a velocity v at the instant shown. However, due to the external magnetic field B it will also be subject to a Lorentz force F as shown (and whose direction can be predicted using Fleming’s Left Hand Rule) which will make it move on an anticlockwise circular path.

Because of the action of the electric field, the magnitude of v will increase meaning that that radius of circulation r of the OH ion will increase. This means that OH ion will travel on an anticlockwise spiral path of gradually increasing radius, as observed. This is analogous to paths followed by charged particles in a cyclotron.

### Observing the circular motion of charged particles in a magnetic field (part 2)

At 0:29 seconds, we observe a second circulation pattern. We see the purple coloured solution begin a clockwise circulation around the anode.

This is because the OH ions gradually move towards the anode and eventually will begin moving at a radial velocity v towards it as shown. Fleming’s Left Hand Rule predicts a Lorentz force F will act on the ion as shown which means that it will move on a clockwise circular path.

The video from 0:30 to 0:35 shows at least some the ions moving on clockwise spiral path of decreasing radius. This is most likely because the magnitude of v of a number of ions is decreasing. The mechanism which produces this decrease of v is unknown (at least to me) but it seems plausible to suppose that a large number of OH ions arriving in the smaller region around the anode might produce a ‘traffic jam’ that would reduce the mean velocity of the ions here.

### Conclusion

I hope physics teachers find this demonstration as useful and intriguing as I do. Please leave a comment if you decide to use it in your physics classroom. Many thanks to Bob Worley for posting the fascinating video!