A point charge lies inside a closed spherical surface of radius centred on the origin

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential

Conditions of Validity, Ch Gauss, Stokes and Green proved, and the first inversion of a differential operator

Problem

A point charge q1=2.0 nCq_1 = 2.0\,\mathrm{nC} lies inside a closed spherical surface SS of radius R=5.0 cmR=5.0\,\mathrm{cm} centred on the origin, at the point (1.0,0,0) cm(1.0,0,0)\,\mathrm{cm}. A second point charge q2=−5.0 nCq_2 = -5.0\,\mathrm{nC} lies outside SS, at (8.0,0,0) cm(8.0,0,0)\,\mathrm{cm}. Each produces an inverse-square field E=q4πϵ0r^′r′2\mathbf E = \dfrac{q}{4\pi\epsilon_0}\dfrac{\hat{\mathbf r}'}{r'^2} about its own location, with ϵ0=8.854×10−12 F m−1\epsilon_0=8.854\times10^{-12}\,\mathrm{F\,m^{-1}}. ((a)) Using excision and superposition, find the total outward flux ∮S(E1+E2)⋅dS\oint_S(\mathbf E_1+\mathbf E_2)\cdot\mathrm d\mathbf S. ((b)) Explain why q2q_2 contributes nothing, even though its field is not zero anywhere on SS.

Browse the problem library