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 Φ 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 θ and θ + dθ is dA = (2 πR sin θ )( R dθ ) = 2 πR 2 sin θ 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. FIGURE 22–50 Problem 66.
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 Φ 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 θ and θ + dθ is dA = (2 πR sin θ )( R dθ ) = 2 πR 2 sin θ 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. FIGURE 22–50 Problem 66.
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 ΦE 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 θ and θ + dθ is dA = (2πR sin θ)(R dθ) = 2πR2sin θ 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.
Achargeofq=−9.0μCisuniformlydistributedaroundaquartercircleofradiusr=12.0cm(seefigure). Find the electric field E at point P located at the center of curvature.
When does the electric flux result to zero?
Find the fluc through the top, left, and right sides of a cube of side 0.5m when placed in a horizontal uniform electric field of 8.0 N/C directed to the right.
Chapter 22 Solutions
Physics for Scientists and Engineers, Books a la Carte Edition
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