Use the image method to make two order-of-magnitude estimates.

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics

The Boundary-Value Problem, Ch Uniqueness, images and the Green function of a region

Problem

Use the image method to make two order-of-magnitude estimates. ((a)) An electron sits a distance d=1.0 nmd = 1.0\,\mathrm{nm} from the flat surface of a large earthed metal sheet. Modelling the sheet as an ideal earthed conducting plane and the electron as a point charge −e-e with e=1.602×10−19 Ce = 1.602\times10^{-19}\,\mathrm{C}, estimate the electrostatic image energy of the electron, in joules and in electron-volts. ((b)) A charged dust grain carrying Q=1.0 pCQ = 1.0\,\mathrm{pC} hovers at a distance b=1.0 cmb = 1.0\,\mathrm{cm} from the centre of an earthed conducting sphere of radius a=2.0 mma = 2.0\,\mathrm{mm}. Estimate the magnitude of the force the sphere exerts on the grain.

Browse the problem library