Two large flat insulating sheets are held parallel to one another
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
Two large flat insulating sheets are held parallel to one another, 60.0mm apart. Their charge is fixed and spread uniformly, with surface densities +1.50×10−6Cm−2 on one sheet and −1.50×10−6Cm−2 on the other. The sheets are wide enough that edge effects are ignored, so each may be treated as an infinite plane. Take an x-axis perpendicular to the sheets, pointing from the positive sheet towards the negative sheet. A point charge q=+3.00nC is held on an insulating support exactly midway between the sheets. Gravity plays no part in what follows.
((a)) Using Gauss's law for a plane, state the magnitude and direction of the field produced by the two sheets alone at a point between them, and its magnitude outside them.
((b)) Using Coulomb's law for the point charge and superposition, find the distance from q, measured along the line through q perpendicular to the sheets, at which the total electric field is zero. Say on which side of q this point lies and check that it falls inside the gap.
((c)) Gauss's law is true for every closed surface drawn in this arrangement. Explain why, even so, it cannot be used to find the total field at a general point of the gap.