A Posteriori

Attempts to grapple with and elucidate empirical knowledge

Science: Not just a vehicle for technology January 10, 2010

Filed under: General Physics,Public Policy — Rāhul @ 00:14
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Modern life is linked inextricably to Science and Technology. Those two words, although very different in origin and meaning are so intertwined today that their history makes interesting reading. The Merriam Webster online dictionary defines Technology as the practical application of knowledge and Science as a system of knowledge covering general truths or laws that is capable of making falsifiable predictions. This definition suggests that Science creates knowledge which then propagates into Technology that is used to enrich our lives. But the relationship between the two is not always so clearly unidirectional.

2009 was celebrated worldwide as the International year of Astronomy because it was the 400th anniversary of the great Italian physicist Galileo Galilei setting about building his “spyglass” which he soon improved to discover the satellites of Jupiter, sun-spots and the phases of Venus. Galileo did all this without a scientific understanding of the propagation of light which had to wait for Isaac Newton. Instead, the technology of the telescope advanced by continued experimentation, enough for Galileo and others to gather sufficient empirical evidence for a then fledgling theory, that the earth is not the centre of the universe.

Against popular belief of the time, Nikolaus Copernicus in the 16th century had proposed that it is the earth that revolves around the sun and not vice-versa. However, it wasn’t until the preponderance of astronomical evidence gathered by telescopic observations a century later that Copernicus could be proved right. The technology of the telescope completed the most important step in the elevation of Copernicus’ proposal to the level of scientific theory. An overwhelming amount of data was gathered, all of which supported Copernicus’ idea over the model placing the earth at the center of the universe, thus convincing all rational sceptics of its merits. In this case, the advance of technology allowed us to see farther and deeper into nature’s mysteries, thus revealing scientific facts.

On the other hand, modern day technologies are inextricably linked to scientific advances. Quantum theory led to our understanding of semiconductor electronics without which the computer industry wouldn’t have taken off. General relativity allowed us to understand gravity well enough to build spacecrafts that put a human being on the moon. Enhanced understanding of the human body and the germ theory of disease led to the design of cures to many infectious diseases. Science and technology, it seems, are advancing together feeding off the achievements in each other, like a system with positive feedbacks. Improved technology allows us to probe further into phenomena that perplex us and lead to scientific theories that help design still better technologies that add value to life. But this relationship between science and technology was not always so close.

Technological advances have been a hallmark of human civilisation throughout history. Our ancestors controlled fire, learned agriculture, invented the wheel and used natural medicines, all by empirical studies that established their utility without any real understanding of the underlying principles. Despite this challenge, technology made tremendous advances, the importance of which is underscored by the fact that historians use technological strides to define particular ages of human history.

Modern Science also had a precursor in history. All ancient civilisations developed natural philosophy to explain the mysteries that surrounded them. While technologies added comfort to life, philosophical inquiry addressed the relentless questions of the mind. But these endeavours did not mesh effectively together to feed off the advances of each other like modern science and technology do. For instance, some schools of Indian philosophy postulated the atomic theory of matter long before it became a scientific theory based on empirical evidence. But the former cannot be called science because it was not based on experiments. The ancient Chinese on the other hand, made practical use of the observation that magnets always tend to align along the same direction, but they did not attempt to explain it using fundamental principles like we do now.

It was only post-renaissance that modern science, as defined by the scientific method, was born. Natural philosophy began to be buttressed by structured falsifiable experiments. Technologies increasingly made use of scientific advances and contributed to them too. This process of co-mingled development has led today to a situation where we cannot imagine excelling in the pursuit of either without also excelling in the other. But what are the consequences of this blurring of differences?

It is easy to see a causal relationship between technology and tangible benefits to society. In a capitalist economy, technological advances can be easily commercialised and the inventors rewarded handsomely. So there is tremendous societal interest in incubating and facilitating technological endeavours. But, science, on the contrary, is more of a personal pursuit. Although it leads  to technologies, its major purpose is to satisfy our innate curiosity and thirst for knowledge. While this is as, if not more, important than material progress, it is difficult to make the case for a result-oriented society to support science for its own sake, purely for the joy of exploration.

Hence, scientists in modern times have tended to use the interlinkages between science and technology and how advances in the former translate into technological marvels in attempts to win more societal support for science. While there is nothing wrong with the reasoning and it has been successful in increasing science funding, the question has to be asked if this is the right approach in the long run. By restricting the utility of science to the narrow channel of technological progress, we risk de-legitimising, in the eyes of society at large, the science that searches for answers to our basic questions.

Space exploration provides one of the best examples for this malaise. Although human beings have always yearned to unlock the mysteries beyond our earth and to go beyond the frontiers of generations past, we have now got used to justifying space missions for their perceived military or medical value. This has affected policy to such a great extent that we choose space stations that add little to our understanding or sense of our place in the universe against grander missions into outer space.

When the pursuit of science is justified in terms of technological dividends, it advances the cause of neither science nor technology. The greatest contributions to technological progress have come from science that is done for its own sake. Taking the long view to appreciate the historical differences between the two and the different purposes they serve in enriching human life can help us put today’s connections between them in perspective. The pursuit of technology and material progress is a choice. But scientific temper and understanding provide succour to the soul and is a necessity. We should be vigilant not to make support for the latter contingent on our desire for the former.

 

All the room at the bottom December 8, 2009

Filed under: General Physics — Rāhul @ 18:42
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In December 1959, 50 years ago this month, Richard Feynman gave a talk to the American Physical Society at Caltech. Titled “There’s plenty of room at the bottom”, it laid out the promise of the as yet unborn field we call today nanotechnology, and challenged physicists to turn their attention to unlocking the consequences of the laws of physics at this small scale. The potential of nanotechnology is widely recognised today and significant efforts and funding are directed to it. On this occasion of the 50th anniversary, I would like to review briefly the orignal talk by Professor Feynman and to explore how it has shaped nanotechnology research.

Feynman starts the talk appreciating the unique journey of an experimentalist who makes the first inroads into a hitherto unreachable field like Kamerlingh Onnes in low temperature physics and proposes as a similar area, the “problem of manipulating and controlling things on a small scale”. He then goes on to lay out the interesting challenge of writing the entire 24 volumes of the Encyclopaedia Britannica on a pinhead by reducing all its writing linearly by a factor of 25000 and in the same vein, of having all the information in the great libraries in a small block that can be carried about. Then, he talks about using codes of a few atoms instead of letters and symbols as a way to compress information to even smaller dimensions, which he illustrates as showing the “plenty of room” that is at the bottom. The central advance in technology that Feynman anticipates would drive all this is a better electron microscope. In 1959, electron microscopes could resolve dimensions as low as 1 nm. He challenges physicists to reduce this to 10 pm, an improvement of 100 times, which will help us look at and manipulate individual atoms.

Throughout the lecture, Feynman only described possibilities that follow the laws of Physics as then understood, but were beyond the realm of technology. He focussed on the effects of miniaturisation on computers. In the 50s, Computers with relatively few circuits filled entire rooms. If all the devices and circuits were to be made at the atomic level, he suggested that we could have computers with far more complicated circuits in a smaller space, which is exactly what we have today. Then, he talked of how the problems of lubrication and heat dissipation would scale in a favourable way at small dimensions. He also talked about the possibility of nanorobots entering the blood stream to conduct surgery, an idea that has since received considerable play in Science Fiction. Adressing the problem of assembling at the nano level, he suggested using a cascade of master-slave connections, either mechanical or electrical, that would progressively assemble at smaller and smaller levels and identified the need to improve the precision of the apparatus at each stage. As the final frontier, he considered the problem of re-arranging atoms themselves so as to create from elements and compounds to minerals and virtually anything. He ended by talking about how the physical laws are very different at such a small scale and announcing prizes for a technology challenge in this direction.

Although his groundbreaking work in Quantum Electrodynamics was well behind him, Professor Feynman didn’t then enjoy the public reputation of the supremely brilliant and erudite yet witty and charming scientist that he does today.  So, it is interesting why so many papers in nanotechnology quote this lecture as the beginning of the field. There is no direct link between the talk and the various advances that came later. But in many ways, Feynman has been prophetic. The electron microscope can today resolve down to 50 pm, which is as good as a biologist needs. Computers have indeed packed more and more circuits, devices and memory into shorter areas and grown powerful and complicated. But his vision of nano-level assembly and surgery don’t seem any closer today than when he talked about them.  In a series of articles this month, Nature Nanotechnology points to how a nascent field looked to this lecture as a focal point which drove the enormous advances that we have seen in the last few decades. While Feynman got a lot right through his crystal ball, he also got some which aren’t right yet!

Through the whole talk, the reader (and the listener, I am sure!) can sense the scientific zeitgeist of the 50s,  which was a reductionist viewpoint where everything could finally be analysed by a set of physical laws. Chemistry, Biology and other studies, it was thought, could eventually be reduced to Physics and once we had all the fundamental physical laws, we could build everything else from them. Although this point of view still holds much water and an incessant romantic sway, it is undeniable that the major advances of the last few decades have been in Biology, Psychology and Neuroscience and even many Physicists are today taking an emergent, rather than reductionist, view of the science. It can be argued that this signifies a failure of the vision and intellectual firepower required to make fundamental advancements. Perhaps, we will again return, with a momentous discovery, to the reductionist viewpoint. But for now, Science continues to look where the light is for the needle lost in the dark and tries to push the frontiers of the lighted area ever so much outwards. Maybe it will be the ability to manipulate things on an atomic scale that will eventually lead us  to the next great leap forward!

 

Heating and Car Mileage November 17, 2009

Filed under: General Physics — Rāhul @ 23:51
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We are all aware of the mileage hit we unwillingly take when we decide to run the AC on a hot day in the car. But, what about the reverse? What effect does running the heater have on petrol mileage? One of my friends recently brought up this topic and it made for some interesting discussion.

I don’t usually use heating in my car in the winter because I am usually dressed warm and my car rides are pretty short anyway. So, I haven’t had the opportunity to try out my hypothesis (to follow) by trying to mimic other conditions and see if I can get more or less miles for a full tank of Petrol if I have heating on. But, I do manage a pretty high mileage for my ’93 Corolla (nearly 30 miles to the gallon in cold weather with 50%ish highway miles), which could be related to my heating preference.

In my analysis below, the key fact to remember is that the mileage achieved by a car is a function of the ambient temperature. At normal ambient temperatures, a controlled quantity of fuel is injected into the cylinder during each cycle, which is then lit up to produce power. But, when temperature is very low, the car lets in a higher quantity of fuel every cycle in an effort to compensate for the lower temperature by having a higher fuel to air ratio. As temperature decreases, the air in the chamber needs to be more rich in fuel for the fuel to burn at the same rate (in terms of power produced per cycle) as at a higher temperature.  So, we see that when ambient temperature goes down, fuel efficiency reduces too. This is the reason why we see a large drop in petrol mileage in cold weather.

Fuel efficiency decreases also when the temperature is very high. But, this has mostly to do with the enhanced cooling needs of the engine and the passengers rather than the the internal combustion engine itself. Cooling requires energy which saps into the fuel efficiency. So, we see that there is a range of optimum ambient temperature when petrol mileage is the highest, on either side of which it tapers off. This is a feature of many systems when it comes to efficiency.

Coming back to the original question, let us look at the effect of heating on mileage is to see how it affects the temperature in the engine. Car heating systems usually work by siphoning off a part of the heat generated in the engine to warm the passenger area. In winter, especially right after the car is started, the temperature in the engine is much below the optimum range. If at this time, some of the heat being generated is diverted to heat up the passenger cabin, it will reduce the fuel mileage. But, if the car had been running for a while and the engine already above the optimum heat range (unlikely in harsh winters and short drives), then the fuel mileage will increase if the engine is cooled by letting some of its heat out. Of course, when the heat is on, there will be a fan which channels the heat as required. This fan is a drain on the engine whatever the temperature. At sufficiently high temperatures, the mileage gain from losing some engine heat is higher than the mileage loss from the fan. But then I am not sure why I would use the heater on such a hot day!

This post goes awry from the stated purpose of the blog. Rather than trying to form scientific conclusions from observed facts, this post tries to use a priori knowledge to predict what will happen. I hope to gather data and a make an a posteriori post on this matter sometime soon. Till then, my hypothesis is that using the heater in winter does reduce fuel mileage although the effect is likely much less than the effect of A/C in summer.

 

Relativity and the Electromagnetic field October 24, 2009

Filed under: General Physics — Rāhul @ 10:50
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This week, I shall continue on the theme of the magnetic field and using a thought experiment prove the complete  interdependence of the electric and magnetic field, which we’ll see to be two ways of looking at the same thing. I first came across this fascinating line of reasoning in the pages of the second volume of the Feynman lectures on Physics, within which I have sought the most revealing wisdom on nature since my undergraduate days.

Consider a wire carrying current I and a charge at a distance l from it. The current will produce a magnetic field around the wire in the right-hand direction. The charge q is in the presence of the magnetic field, as shown in Fig: 1 below.

Fig: 1 Wire at rest, Charge moving down

Fig: 1 Wire at rest, Charge moving down

Let us consider now that q is moving in a downward direction (note that current is in the upward direction) at a velocity equal to the drift velocity of electrons in the wire carrying current. Now, we shall analyse the forces on the system from two different inertial frames of reference and consider whether the observable results are the same, a requirement that is critical if we are to have any confidence in our methods of analyses. If our physical theory predicts different realities for observers in different inertial frames of reference, that would be a significant shortcoming indeed in the theory.

The first frame of reference is the one in which the wire is at rest. The current I is moving upwards and hence the drift electrons are moving downwards, say with a velocity v. The charge outside the wire, in its magnetic field is also moving down with the same velocity v. Since the wire is neutral, there is no electric force between it and the charge. But, since the charge moves in a magnetic field with a component of its velocity perpendicular to the field, there is a magnetic force on the charge. In this case, using the left hand rule, the force is towards the right if q is a positive charge and towards the left if q is negative. Assuming a positive q, observers in this frame of reference see the charge repelled from the wire. So, its velocity which was initially downwards, would now diverge away from the wire.

Let us now consider another frame of reference, this one moving at the same velocity as the charge and the drift electrons in the wire, as shown in Fig: 2 below.

Fig: 2 Wire moving up, Charge at rest

Fig: 2 Wire moving up, Charge at rest

This would be like imagining the observer in a vessel moving downwards parallel to the motion of the external charge and the wire. In this frame of reference, the drift electrons are at rest and so there is no current in the wire. Hence, there is no magnetic field around the wire and no magnetic force on the charge. Does this mean the charge is at rest in this frame of reference? If so, in the previous frame, the charge should be seen as moving down at a constant velocity v. But, we had seen that the charge diverges away from the wire as it moves down. Since the observations in the two inertial frames have to agree with each other, there has to be something wrong with our reasoning in at least one frame.

In the second frame, since the charge is not moving, there is no magnetic force on it.  Maybe there is another force equivalent to the magnetic force in the first frame that will produce the same effect? One difference between the frames that we have ignored till now is that the wire is moving upward in the second frame and the electrons are at rest, while in the first frame, the wire is at rest and the electrons are moving down. When there is no current through the wire, the electrons and rest of the wire are at rest in the same frame and the charges balance each other. When there is a current and the electrons move downwards and wire is at rest, as in the first frame, according to special relativity, the charge of the electrons is unaffected by the velocity. But, the volume they occupy shrinks because the length of this space along the direction of the velocity shrinks according to the famous Lorentz transformation. Hence the charge density of electrons as seen in the first frame is higher than that in the second frame. By using a similar argument, we can see that the charge density of the positive charges in the wire is higher by the same amount, but in the second frame. So, we see that the second frame sees the wire as charged more positively than the first frame. In the first frame, we know that the wire is neutral. Otherwise, a wire will spontaneously attract or repel charges in its neighbourhood when the current through it is switched on. We see enough current carrying wires in common life to know this is not true. Hence, in the second frame, the wire is positively charged. As the charge q is also positive, it will be repelled from the wire. So, when we take the electric force also into consideration, the charge in the second frame repels from the wire, which when combined with the relative velocity of the second frame downwards with respect to the first, agrees with the observation in the first frame that the charge moved downwards in a divergent manner from the wire.

Similar observations in terms of velocity is arrived at  in both the frames of reference when we consider the effects of the electric and magnetic fields together. This adds to our understanding that they are but two facets of the general electromagnetic field. In different inertial frames, the electromagnetic field splits into different portions of electric and magneric fields and hence forces due to them. In our example, by choosing extremes of frames in which either the wire or the electrons were at rest, we could split the field into just the electric or just the magnetic field. But, many times it is a combination of both. By sacrificing a mathematical treatment of the problem, we have missed out on much elegance for the sake of simplicity. We also don’t know whether the velocities of the electron as seen in both the frames will agree in magnitude as well as in direction. They actually do, and they do this by having forces different in each frame in such a way as to have the velocities the same! I shall explore a mathematical treatment of the problem, again derived from Feynman’s lectures (Section 13-6), in a later post.

 

Why the left hand rule? October 11, 2009

Filed under: General Physics — Rāhul @ 22:57
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Today’s post is about the magnetic field and what it really means in the context of the force felt by a charge moving through it. From high school physics, we know that a moving charge (0r current) in a magnetic field feels a certain force on it which is perpendicular both to the direction of motion and the direction of the magnetic field. To find out the direction of this force, we can either follow through with the vector cross product of the current and the magnetic field or use one of the many hand tricks like the left hand rule below.

Fig: 1 Left hand rule

Fig: 1 Left hand rule

The first question that comes to my mind really is, what is magnetic field? A moving charge as well as the effects of force in motion are both observables. But, how do we observe the magnetic field? If we don’t, how do we know it is there? The magnetic field, like other fields, is a creation of science, not nature. We use it to help explain observables like current and acceleration.

Let’s assume there are magnets as shown in Fig:1, between which is a conductor carrying current in the direction shown. Then, we observe a force on the conductor in the upward direction. We observe that when the magnets are removed from the picture, there is no longer a force on the conductor. Also, when one of the magnets is flipped so that they are repelling, there is no force on the conductor. But, when both the magnets are flipped so that they attract again, we see that the force on the conductor is now of the same intensity as the first case, but downwards. If we are to define two poles for a magnet- north and south and imaginary lines emanating from the north pole and sinking into the south pole, we see that there are such lines crossing the conductor only when there is a north pole and a south pole on either side of it and this, we might hypothesise, encapsulates the effect of the magnet on the conductor. So, the idea of the magnetic field (it it works) replaces the whole structure of the magnets with one space and time variant vector, as far as the current carrying conductor is concerned.

As myriad experiments prove the utility of the magnetic field idea and validates our left hand rule, we still don’t know if this is the best method to reduce the effects of the magnets. We see that this definition of magnetic field is perpendicular both to the current and the direction of force, the two directions where there are observable effects. Why not define the magnetic field in the direction of the force like the electric field or gravitational field is? To explore why, let us use the method of contradictions. Assuming the direction of magnetic field is defined along the force on the conductor, we see that the current is perpendicular to both the magnetic field and the force which lie along the same axis. If the current is now flipped, the force, according to the previous rule will still be along the same direction as it remains perpendicular to current and parallel to the magnetic field. But, we observe that when the direction of current is flipped, so is the direction of the force on the conductor. So, we cannot define magnetic field in the direction of the force. We can also rule out defining it in the direction of the current because then, we do not have any easy way to judge the direction of force, apart from restricting it to a plane perpendicular to the current and field. But, if we do choose a direction orthogonal to both the current and force, we see that simple rules like the left hand rule can be developed to find one observable from the other in a way that agrees with experiment.

While all fields are human creations, I have always found the idea of the magnetic field the most artificial. I don’t have any rational arguments for this feeling, but it has to do with how it is defined in a direction which is apart from either of the observable vectors involved. But, as we see, this is the only way we see how to define the magnetic field in a way that facilitates accurate predictions between current and force.

 

Jump not to conclusions September 30, 2009

Filed under: General Physics — Rāhul @ 11:52
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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
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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.