Question

1. Please answer the following questions.

? What is the origin of electric resistance in material? Please give an argument to explain why capacitance depends on the geometry of the capacitor. (5%)

? Is Ampère’s law valid for the straight wire with finite length? Give an example to explain your answer using the Biot-Savart Law. (5%)

Answer 1

a) The electrical resistance of a conductor which is given by R=V/I is analogous to the the pressure between 2 ends of a pipe along which water is flowing. Just as the resistance of the pipe to the flow of water in it depends on the length, width etc. of the pipe so also the electrical resistance of the conductor is determined by analogous characteristics.

An analogy can be made between a capacitor carrying a charge q and a rigid container of volume V containing moles of an ideal gas. We have .For the capacitor q=(C)V.

Thus the capacitance C of the capacitor is analogous to the volume of the container. This gives us an explanation why the capacitance depends on the geometry of the capacitor.

b) Ampere's law applies only to ideal cases wherein there are symmetrical distributions of current as it is deduced from the mathematical theory of vector fields while Biot -Savart's being determined from experiment is applicable to real or non-symmetrical distributions of current.Thus Ampere's law is not perfectly valid for a straight wire with finite length but only to the ideal case of a wire with infinite length.