PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential
Electricity, Magnetism and Electromagnetism, Ch Electric charge, Coulomb's law and the electric field
Problem
A thin flat annulus, a disc of outer radius R=8.0cm with a central hole of radius a=3.0cm, carries the uniform surface charge density σ=+2.5×10−7Cm−2 on the part between the two radii. It lies in the xy-plane with its centre at the origin, so its axis is the z-axis. Two point charges, each of −4.0nC, are held on that axis, one at z=+6.0cm and one at z=−6.0cm. Everything is in vacuum and all the charges are held fixed.
((a)) Treat the annulus as a set of thin rings of radius r and width dr. Set up the integral over these rings for the axial field of the annulus at height z>0, evaluate it, and find the field of the annulus alone at the point P on the axis at z=+3.0cm.
((b)) Find the magnitude and direction of the net field at P.
((c)) Find the force on a small charge q0=+1.5nC placed at P.