Simple Nature - Light and Matter

Discussion Questionsg / Discussion question A-D.A One question that might naturally occur to you about Gauss’s lawis what happens for charge that is exactly on the surface — should it becounted toward the enclosed charge, or not? If charges can be perfect,infinitesimal points, then this could be a physically meaningful question.Suppose we approach this question by way of a limit: start with charge qspread out over a sphere of finite size, and then make the size of thesphere approach zero. The figure shows a uniformly charged spherethat’s exactly half-way in and half-way out of the cubical Gaussian surface.What is the flux through the cube, compared to what it would be ifthe charge was entirely enclosed? (There are at least three ways to findthis flux: by direct integration, by Gauss’s law, or by the additivity of fluxby region.)B The dipole is completely enclosed in the cube. What does Gauss’slaw say about the flux through the cube? If you imagine the dipole’s fieldpattern, can you verify that this makes sense?C The wire passes in through one side of the cube and out throughthe other. If the current through the wire is increasing, then the wire willact like an inductor, and there will be a voltage difference between itsends. (The inductance will be relatively small, since the wire isn’t coiledup, and the ∆V will therefore also be fairly small, but still not zero.) The∆V implies the existence of electric fields, and yet Gauss’s law says theflux must be zero, since there is no charge inside the cube. Why isn’tGauss’s law violated?D The charge has been loitering near the edge of the cube, but isthen suddenly hit with a mallet, causing it to fly off toward the left sideof the cube. We haven’t yet discussed in detail how disturbances in theelectric and magnetic fields ripple outward through space, but it turns outthat they do so at the speed of light. (In fact, that’s what light is: ripplesin the electric and magnetic fields.) Because the charge is closer to theleft side of the cube, the change in the electric field occurs there before624 Chapter 10 Fields