A hemisphere of radius R is placed in a charge-free
Chapter 22, Problem 22.66(choose chapter or problem)
A hemisphere of radius R is placed in a charge-free regionof space where a uniform electric field exists of magnitudeE directed perpendicular to the hemispheres circular base(Fig. 22-50). (a) Using the definition of through anopen surface, calculate (via explicit integration) theelectric flux through the hemisphere. [Hint: In Fig. 22-50you can see that, on the surface of a sphere, the infinitesimalarea located between the angles 0 and 0 + dd isdA = (2ttR sin 6)(Rdd) = 2ttR2 sin 6 d0.\ (b) Choose anappropriate gaussiansurface and use Gaussslaw to much more easilyobtain the same resultfor the electric fluxthrough the hemisphere.FIGURE 22-50 66.
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