A thin ring of radius carries a charge spread uniformly around it

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 ring of radius R=5.00 cmR = 5.00\,\mathrm{cm} carries a charge Q=+8.00 nCQ = +8.00\,\mathrm{nC} spread uniformly around it. The ring lies in the xyxy-plane with its centre at the origin, so its axis is the zz-axis. A point charge q1=−4.00 nCq_1 = -4.00\,\mathrm{nC} is held at the centre of the ring. Everything is in vacuum, all of these charges are held fixed, and the ring's charge stays uniformly spread. ((a)) Find the magnitude and direction of the electric field at the point PP on the axis at z=+12.0 cmz = +12.0\,\mathrm{cm}. ((b)) A small charge q0=+2.00 nCq_0 = +2.00\,\mathrm{nC} is now placed at PP. Find the magnitude and direction of the force on it.

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