A hemisphere of radius R is placed in a
charge-free region of space where a uniform electric field...

Question

A hemisphere of radius R is placed in a
charge-free region of space where a uniform electric field exists of magnitude
E directed perpendicular to the hemisphere’s circular base (Fig. 22–50). (a)
Using the definition of E through an “open” surface, calculate (via explicit integration) the
electric flux through the hemisphere. [Hint: In Fig. 22–50 you can see that, on
the surface of a sphere, the infinitesimal area located between the angles  and  + d is  (b) Choose an appropriate gaussian surface and use Gauss’s law to
much more easily obtain the same result for the electric flux through the
hemisphere.



FIGURE 22–50

Baljit · Accepted Answer

A hemisphere of radius R is placed in a charge-free region of space where a uniform electric field exists of magnitude E directed perpendicular to the hemisphere’s circular base (Fig. 22–50). 
(a) Using the definition of through ɸE  an “open” surface, calculate (via explicit integration) the electric flux through the hemisphere. [Hint: In Fig. 22–50 you can see that, on the surface of a sphere, the infinitesimal area located between the angles θ and θ+dθ is 
dA=(2πR Sinθ)(R dθ )=2πR2 Sinθ  dθ
 (b) Choose an appropriate gaussian surface and use Gauss’s law to much more easily obtain the same result for the electric flux through the hemisphere.

A hemisphere of radius R is placed in a charge-free region of space where a uniform electric field exists of magnitude E directed perpendicular to the hemisphere’s circular base (Fig. 22–50). (a)...

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