# A Posteriori

## Attempts to grapple with and elucidate empirical knowledge

### Charges on sticky tapes September 17, 2009

Filed under: General Physics — Rāhul @ 12:08
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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

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

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!