Question

Please do part (b) and (c).

Question 1 [9 + 3 + 3 = 15 marks] (a) The inside of a resting nerve cell (an axon) is -90 mV with respect to the outside. Assume that the cell can be modelled as two planar sheets of surface charge of opposite sign separated by a small distance. Determine the numerical value of the dipole moment per unit area of the cell. (Take the permittivity of the region between the sheets of surface charge to be so). (b) Explain why the Meissner effect seen in superconductors can be used to levitate a magnet. (c) Discuss the differences between the electromagnetic properties of perfect conductors and of superconductors for which the Meissner effect is observed.

Answer 1

b)Superconductors are materials that conduct electric current with no resistance. Electrical resistance is the property of a material to oppose current passing through and is found in nearly everything from light bulb filaments to your own body. Superconductivity occurs at extremely low temperatures and induces, or creates, a strong magnetic field. The current that flows at the surface of the superconducting material creates these magnetic fields. Inside the superconductor, the magnetic fields are cancelled out, but outside they are strong and can levitate a magnet.

c)

Perfect conductors:

• have exactly zero electrical resistance - a steady current within a perfect conductor will flow without losing energy to resistance. Resistance is what causes heating in conductors, thus a perfect conductor will generate no heat. Since energy is not being lost to heat, the current will not dissipate; it will flow indefinitely within the perfect conductor until there exists no potential difference.
• require a constant magnetic flux - the magnetic flux within the perfect conductor must be constant with time. Any external field applied to a perfect conductor will have no effect on its internal field configuration.

  Superconductors,in addition to having no electrical resistance, exhibit quantum effects such as the Meissner effect and quantization of magnetic flux.

  In perfect conductors, the interior magnetic field must remain fixed but can have a zero or nonzero value.In real superconductors, all magnetic flux is expelled during the phase transition to superconductivity (the Meissner effect), and the magnetic field is always zero within the bulk of the superconductor.