An insulating disc of radius carries a fixed charge spread uniformly over one face…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential
Electricity, Magnetism and Electromagnetism, Ch Electric flux and Gauss's law
Problem
An insulating disc of radius R=0.150m carries a fixed charge spread uniformly over one face with surface density σ=2.00×10−7Cm−2.
((a)) Two very large parallel insulating sheets carry uniform surface densities +2.00×10−7 and −2.00×10−7Cm−2, and are treated as infinite planes. Using Gauss's law, give the magnitude of the field between them and the magnitude outside them.
((b)) Now return to the single finite disc, on its own in otherwise empty space. Using the Chapter 1 result for the field on the axis of a uniformly charged disc, built by summing thin rings, find the magnitude and direction of the field on the axis at a distance z=50.0mm from the centre of the disc.
((c)) Express your answer to (b) as a fraction of the infinite-plane value σ/2ε0 for the same σ.
((d)) The flux of the disc's field out of any closed surface drawn around it is Q/ε0, with Q the disc's charge. Explain why Gauss's law nevertheless cannot deliver the answer to (b).