Paper 1, Section II, D

Electromagnetism
Part IB, 2011

Starting from the relevant Maxwell equation, derive Gauss's law in integral form.

Use Gauss's law to obtain the potential at a distance rr from an infinite straight wire with charge λ\lambda per unit length.

Write down the potential due to two infinite wires parallel to the zz-axis, one at x=y=0x=y=0 with charge λ\lambda per unit length and the other at x=0,y=dx=0, y=d with charge λ-\lambda per unit length.

Find the potential and the electric field in the limit d0d \rightarrow 0 with λd=p\lambda d=p where pp is fixed. Sketch the equipotentials and the electric field lines.