Simple Nature - Light and Matter

c/Each part of the surface has its own area vector. Note the differences in lengths of the vectors, corresponding to the unequal ...

|E|= kqtotal r^2 , whereris the radius of Flatcat. The flux is then Φ = ∑ Ej·Aj, and since theEjandAjvectors are parallel, the d ...

e/1. The flux due to two charges equals the sum of the fluxes from each one. 2. When two regions are joined together, the flux t ...

f/The flux through a tiny cube due to a point charge. by considering its point charges individually, and the additivity-by- regi ...

extended to the case where the charge is not along any axis of the cube,^11 and based on additivity we then have a proof that th ...

Discussion Questions g/Discussion question A-D. A One question that might naturally occur to you about Gauss’s law is what happe ...

h/Completing the proof of Gauss’ theorem. the information reaches the right side. This would seem certain to lead to a violation ...

i/Applying Gauss’ law to an infinite line of charge. with charge, change the Coulomb constantkto the gravitational constantG, an ...

j/Applying Gauss’ law to an infinite charged surface. shown in the figure. The length,L, of the surface is irrelevant. The field ...

The symmetry between the two sides could be broken by the existence of other charges nearby, whose fields would add onto the fie ...

a/A tiny cubical Gaussian surface. 10.7 Gauss’ law in differential form 10.7.1 Gauss’s law as a local law Gauss’ law is a bit sp ...

b/A meter for measuring divE. c/Example 39. where dvis the volume of the cube. In evaluating each of these three derivatives, we ...

Mathematically, let thexaxis be to the right and letybe up. The field is of the form E= (sinK x)ˆy, where the constantK is not t ...

Straightforward algebra shows that adding in the other two terms results in zero, which makes sense, because there is no charge ...

d/Discussion question A. This can indeed be constant, but only ifnis 0 or−3, i.e.,pis 1 or−2. The second solution gives a diverg ...

e/The method of images. q. The field in the vacuum surroundingqwill be a sum of fields due toqand fields due to these charges in ...

Problems The symbols √ , , etc. are explained on page 668. 1 The gap between the electrodes in an automobile engine’s spark plug ...

Problem 8. Problem 11. Problem 13. (b) Generalize the result of part a to any pair of charges with equal magnitude and opposite ...

Problem 19. Problem 20. proton, for example, the field is very strong. To see this, think of the electron as a spherically symme ...

Problem 23. locationsx=±b,y=±bof the four points on the surfaces that are closest to the central axis.) There is no obvious, ped ...