The purpose of today's activity is to play with magnets and materials in a structured way. Students will be provided a supply of magnets and materials and asked to try to determine various features of magnetic interactions. Among the features are: (a) distance dependence of interaction force; (b) screening, enhancing, and redirecting of magnetic forces by materials; (c) creation of surprising motion of other objects.
Notes on Pendulum
Students are asked to work with a pendulum to gather qualitative information about magnetic interactions and the ability of other materials to enhance or diminish the interaction between two magnets. The pendulum will achieve, at best, unstable equilibrium during the activity. The students may notice that the pendulum angle from the vertical can be made larger without changing the separation of the magnets. Stable equilibrium is needed to get reliable quantitative relationships between the magnitude of the force and the separation between two magnets. Further complicating the problem is the non-uniformity of the magnetic fields for which the observations are collected. The reason is that the magnetic force has both vertical and horizontal components. Without detailed knowledge of the vector direction of the magnetic fields in the problem, knowledge of the magnitude of the tension force is required to extract the strength of the magnetic interaction from the problem. This is a fairly straightforward application of Newton's Second Law. Indeed, this forms a nice exercise in experimental design as informed by theoretical consideration.
Notes on Pencil and Washer Force Determination
Students are asked to place ring magnets on a vertical pencil such that some are levitated above the others. Students will measure the separation between the magnets while adding washers to the top magnet thereby increasing the supported mass. The total gravitational force of the upper magnet/washer set gives the magnitude of the magnetic interaction. A graph of the mass supported as a function of the separation of the two magnets will show an inverse dependence of magnetic interaction strength on separation. Static friction, uniformity of magnets, uniformity of mass distribution, and reading of ruler are leading experimental errors. The overall goal is to develop a plot revealing the inverse dependence of strength on separation.
Quantitative measurement of forces, without force probes and spring scales is a bit difficult. The chief reason is Earnshaw's Theorem:
"The so-called Earnshaw's theorem explicitly states that, however hard you try, it is impossible to achieve stable levitation of a magnet in a system governed by stationary electric, magnetic and gravitational forces."The above quote is from a web article at http://www.sci.kun.nl/hfml/fingertip.html
Yet, we find that levitation is possible if certain types of materials (dimagnets) are used:
A dimagnetic material produces a magnetic field that opposes an external field. A paramagnetic materia, on the other hand, produces a magnetic field that increases an external field. Dimagnetism and paramagnetism are induced when an object is placed in a magnetic field. Without an external field, the effects are not seen. To be complete, there is a third type of material: ferromagnetic. Ferromagnetic materials are natural producers of magnetic fields like iron, cobalt, and nickel.
The reality of dimagnetism is that it usually takes very strong external fields to produce the effect. Some researchers have been able to levitate frogs (http://www.sci.kun.nl/hfml/froglev.html) without harming them in fields of 16 Tesla (1000 times stronger than the typical refrigerator magnet). Dimagnetic levitation is not easy to produce in student labs because of material and set-up considerations. If you would like to try, a detailed but reasonably straightforward procedure is given at http://scitoys.com/scitoys/scitoys/magnets/suspension.html.
Students are asked to discover if intervening materials 'affect' the interaction of magnets. They most certainly do! While gravitation cannot be screened or hidden from the observer (we would be able to detect Darth Vader's Death Star lurking behind the sun as an increase in the gravitational field affecting the earth and satellites!), electrostatic and magnetic forces can be screened or hidden from the observer. This involves the fundamental source of magnetic phenomena: charged particles are in motion in all matter. What creates a magnetic field must also detect one (Newton's Third Law). Thus, detection and creation become a complicated sequence of events with a natural feedback mechanism (Lenz's Law). While the material here does not address the issue, magnetism is not a conservative force yet various quantities (such as the amount of field passing through a unit of area) are conserved.
Whether students observe both screening and enhancing effects is a function of
the care with which students make observations and the types of materials they
have available. A metal coffee or juice can lid will enhance local fields by
contributing to them. A bit of plastic or a balloon, given a static charge,
will alter the local magnetic field when it is in motion. The students ought
to discover this with their magnetometers.