Homework 10

E&M 6.5, 6.7, 6.9, 6.10, 6.14, 7.1, 7.5, 7.7

9) If magnetic monopoles existed, which of Maxwell's equations would be altered and what would be their new form? You should use Q_m for the conserved magnetic charge corresponding to Q for an electric charge and similar names for other quantities (e.g. magnetic current density would be J_m).

10) Consider a parallel plate capacitor with circular plates of radius R placed a distance d apart. They are connected at their centres to straight wires that extend perpendicularly from the plates.

a) Show that the magnetic field at a radius r out side the capacitor plates (that is r > R) is given by
B=μ₀ID
      2πr
where ID is the displacement current.
b) This equation has the same form as that for the field outside the wire leading to the capacitor, why?
c) Compare the magnetic field between the plates with the field outside the wire. Calculate both fields at the same radius r > R. Discuss whether this makes sense.
d) What can you say about the relative strengths of the fields inside the capacitor and outside the wire for radii r < R?