A Posteriori

Attempts to grapple with and elucidate empirical knowledge

Jump not to conclusions September 30, 2009

Filed under: General Physics — Rāhul @ 11:52
Tags: ,

Today’s post is on why it isn’t wise in science to jump to conclusions, at least not ones which we’re too hasty to take as facts. Yesterday, I was in the cleanroom, cleaning some wafer pieces for SIMS analysis. My samples were being cleaned at high temperature in a water bath, when I noticed something interesting. I whisked out my phone and got some pictures to illustrate my points.

I had 3 small beakers in the water bath, almost evenly spaced out, as shown in Fig: 1 below.

Beakers immersed in water bath with even spacing

Fig: 1 Beakers immersed in water bath at even spacing

After about 10 minutes, I noticed that beakers had migrated within the water bath to cluster together at one end, as shown below in Fig: 2.

Fig: 2 Beakers clustered together in the water bath

Fig: 2 Beakers clustered together in the water bath

The water was at about 80 degrees centigrade and the various stresses in it was creating many eddies and waves, but the question was why there was a net. effect towards clustering the beakers. I wondered if there was some reason why the forces on the beaker surface would vary in magnitude based on the amount of water beyond it. This might mean that the beakers will tend to cluster closer together as the greater force from the larger quantity of water outside the cluster than the force from inside the cluster would push them together. This would also explain why in Fig: 2, all three beakers didn’t move to the center of the water bath. There water-force proportionality argument works to keep the beakers closer to the edge of the water bath too.

I started exploring reasons why the quantity of water in the neighbourhood might affect the force on the beakers and cause clustering, but could not come up with any satisfactory answer. After all, the bombardment of high energy water molecules on the surface of the beaker (pressure) is just a function of the local temperature. Although temperature might vary radially in the water bath, that wouldn’t explain the behaviour. So, my hypothesis was proving hard to substantiate, even with the limited physics I employed. Then, I thought that maybe there is a gradient along the water bath towards the far side so that beakers move that way because gravity can overcome friction on the beakers when there is random agitation of water. To test this, I replaced the beakers as shown in Fig: 3 below.

Fig: 3 Beakers placed together on the near side

Fig: 3 Beakers placed together on the near side

If the reason for the 3 beakers in Figs 1 and 2 clustering on the far side was an effective force bringing them together, then, the beakers should now remain clustered. But, after a short while, the beakers moved as shown in Fig: 4 below.

Fig: 4 Beakers moving to the far side

Fig: 4 Beakers moving to the far side

The glass beakers moved over to the far side of the water bath while the Teflon beaker remains steady. We don’t know if this difference is related to the material or weight of the beakers or just due to their relative positions. But, from this observation, we can indeed reject any tendency to clusterise as the main reason why the beakers in Figs 1 and 2 moved over to the far side. There does seem to be a gravitational (or other) gradient favouring the far side of the water bath.  Even if there is a force favouring clustering, the gravitational gradient overcomes it, as seen in Figs 3 and 4. The Teflon beaker might not have moved to the far side in Fig: 4 because of a local energy minimum there. But, I am not certain because it was time for me to remove my samples from the water bath, and hence my experiments with the beakers had to cease!

This post just intends to illustrate why in Science we should remain ever-vigilant in seeking new information and never too dogmatic to re-evaluate the theories we might find interesting. My former theory sounded more fun to me, but further evidence pointed to something more prosaic. Prosaic, yet agreeing with evidence!


Rod, sphere and foil bit September 20, 2009

Filed under: General Physics — Rāhul @ 14:33
Tags: , ,

Today’s post continues on the experimental electrostatics theme from the previous post. We notice charge induction by polarisation and a neat way to distinguish between conductors and insulators through a definite observation that doesn’t rely on measurements or intricate apparatus.

Fig: 1 Rod, conductor and foil bit

Fig: 1 Rod, conductor and foil bit

In Fig: 1 above, there is a charged rod, a brass sphere mounted on top of an insulating stand and a conducting foil bit suspended by an insulating string. The rod is charged by rubbing with fake fur, where the abrasion causes exchange of charges. The brass sphere and foil bit are both momentarily grounded by touching with fingers. When the rod is brought close to the sphere as shown, it is observed that the foil bit is attracted to the sphere, and after making contact, repelled strongly. The string attached to the foil bit now makes a noticeable angle with the vertical, signifying the strength of repulsion.

To explain this, let us assume that the charged plastic rod carries a negative charge. As this approaches the neutral brass sphere, it polarises the charges in the sphere. Since brass is a metallic alloy, we can assume the electrons to be free to move around in a lattice of positively charged ions. In this case, the electrons feel a force or repulsion from the net. negative charge of the plastic rod and they are redistributed on the surface of the sphere in a manner that balances the repulsion between the concentrated electrons on the right side and the repulsion from the rod on the left. In a very short time (nearly instantaneous to our observation) the centre of charge of the electrons shifts to the right of the sphere. The right side of the sphere now carries a net negative charge whereas the left side carries a net. positive charge, making it an effective dipole. Since the brass mass rests on an insulating stand, any local excess of charge on it is not grounded. The same applies to the aluminium foil bit which hangs on an insulating string.

The brass sphere dipole polarises the charged bit by repelling the electrons in the aluminium foil to the far side and making the latter an effective dipole too. Although the former polarisation was from an object with an excess charge, and the latter from an object which is a neutral dipole, the effect is similar. This accentuates the point that electrostatic force, which seeming to act at a distance, is only a consequence of local effects that build up. In both cases in this experiment, there is a difference in the kind of charges perceived, which can also be thought of as the net. electric field. The polarised aluminium foil is attracted to the brass sphere because after polarisation, the unlike charges are closer and hence the force between them stronger than the like charges. There was also a force between the sphere and the charged rod, but not enough to overcome the restraints on them. The foil bit, on the other hand, moves to touch the right side of the sphere. Since they are both conductors, there is a redistribution of charge between the negatively charged right side of the sphere and positively charged left side of the foil bit. This reduces the negative charge on the right side of the sphere a little, but the foil bit still sees it as a negative charge. But, the charge on the foil bit was not as high to start with and the redistribution left it with so much net negative charge that the brass sphere now sees it as a negative charge. Hence, they repel.

From our explanation, we can see that for the latter repulsion to occur, the charge content on the foil bit should be much less than the brass sphere. This is ensured by their sizes and the weakening of charge induction as we move down the chain. Finally, if we are to touch the negatively charged foil bit with a finger, its excess charge will instantly be grounded and it will be polarised by and attracted to the brass sphere again. The attraction to and repulsion from the sphere will produce an oscillation of the foil bit between the sphere and the finger, as charge moves from the sphere through the bit and the finger to ground. This loss of negative charge makes the sphere progressively more positively charged. If the charged rod were pulled away from the brass sphere, the polarisation on the sphere will be lost and the oscillation will eventually die down when the charge on the sphere is lost.

The above explanation would work just as well if we had called the charge on the rod positive. While the charges on the rest of the objects will change too, the motions and other observables will be unchanged. We also need to remember that the definitions of conductor and insulator are subjective to the application. There is no strict demarcation between them, at least not one that is accepted in every case. Finally, I stress that our explanation above is by no means complete. It is just something that is not falsified by experiment, seems to fit the facts and our knowledge of electrostatics and is not too hard for me to understand. The acceptance that there is a deeper understanding that currently eludes us is not necessarily discouraging. There is still beauty in the patterns that we do discern in nature and still intrigue in searching for more beautiful ones further.


Charges on sticky tapes September 17, 2009

Filed under: General Physics — Rāhul @ 12:08
Tags: , ,

Since I am teaching undergraduate physics labs this semester, I shall try to include simple yet interesting observations and try to explore the laws underlying them.

Today’s experiments are classical discovery experiments. We assume that there are physical quantities we call charges which are conserved and that charges are of two kinds which we define as positive and negative. Quite like mass, we assume also that all bodies in common macroscopic experience have positive and negative charges within them and the numbers of these two kinds of charge units decide whether the bodies have a net. positive, negative or neutral charge.

The first observation involves two scotch tapes. At first, we notice that there is no perceptible force between two freshly cut strips of scotch tape. Then, one of the ends of each scotch tape is stuck on a flat wooden surface so that they are close to each other and pulled off quickly in similar fashion. When they are brought close to each other, we see that the ends of the tape which were stuck on and then pulled off the wood repel irrespective of whether the sticky or the non-sticky side is facing the other tape. But, there is no repulsion between the free ends of the tape.

Fig: 1 Repulsion between similarly charged ends of scotch tape

Fig: 1 Repulsion between similarly charged ends of scotch tape

From these observations, we can conclude that sticking on and tearing off wood caused two strips of scotch tape which otherwise don’t experience any force between each other, to repel. Since we know that matter contains charges, perhaps some charges were exchanged between the scotch tape and the wood when the tape was pulled off? This would leave the tape with an imbalance between positive and negative charges, depending on how much of what kind of charges were exchanged and hence the tape would be charged, either positively or negatively. Whether positive or negative, we are sure that the ends of both the strips would be charged as the same kind because they were both first neutral and pulled off the table in the same way.

The line of reasoning in the previous paragraph supports a tentative assertion that like charges repel each other. It is important to remember that there are many other explanations which are supported as well or perhaps better by our observation. It is only by carrying out multiple experiments to control for other factors which might be causing the observed results that we gain confidence in our assertion that like charges repel. Let us assume that multiple experiments over the centuries have convinced us to a great extent. Let us now see if we can use this knowledge to understand more about the forces between charges. What, if any, would be the force between two unlike charges?

We take two strips of scotch tape again and stick one (called b) on to the same wooden surface as before. The second strip (called t) is then stuck on top of b such that t sticks only to b and doesn’t overlap onto the wooden surface. Then, b is pulled off the wooden surface just like in the previous experiment (with t still stuck on b). So, we know that b is charged either positive or negative. t and b are then pulled apart quickly and brought close to each other. It is observed that they attract each other now.

Fig: 2 Attraction between oppositely charged ends of scotch tape

Fig: 2 Attraction between oppositely charged ends of scotch tape

When the t tape was pulled off b, we hypothesise again that some charges were exchanged between b and t. Since charge is conserved, which means that charge can only be transferred but not created or destroyed, all the charge that t newly acquired must be at the expense of b. Let us assume that pulling off the wood gave b a charge of q. If t now acquires a charge of p, then b should have remaining a charge of q-p. Since b and p don’t repel, we know that they don’t have the same kind of net.charge. One is positively charged and the other is negatively charged. We also observe here that these unlike charges attract. Like before, we aren’t yet sure of our explanation. It is only one of the many valid hypotheses, but one that has stood the test of time over many centuries.

While we observed the attraction between unlike charges, it is not necessary to obtain unlike charges in the previous case. If we define q > 0, then 0 < p < q together with p > 0 means we have like charges which are both positive. By inverting the definition, we could have charges that are both negative. But, since the charge transfer between the two scotch tape strips (p) either added to q or took away from q enough to make it in both cases unlike p, we observed attraction and not repulsion.

From both of the experiments above, we cannot yet tell which charge is positive and which is negative. For that, we first need a definition of a negative and positive charge. The most elementary charge is that of an electron, which is defined negative. By using measurement instruments calibrated against this definition, we can find out which of t or b has a negative or positive charge!