A thin spherical shell of radius 20.0 cm has 5.0 µC of charge uniformly distributed over its surface. What is the electric flux through an area of 1.00 m2 of a spherical surface concentric with the shell of charge but having a radius of 1.00 m?
a) 5.6x105 N·m2/C
b) 4.5x104 N·m2/C
c) 1.8x104 N·m2/C
d) 2.3x105 N·m2/C
e) 0
a) 5.6x105 N·m2/C
b) 4.5x104 N·m2/C
c) 1.8x104 N·m2/C
d) 2.3x105 N·m2/C
e) 0
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Gauss' law: total flux = closed-surface integral of E = Q/e0, e0 = 8.85e-12 SI, Q = 5e-6C
Shell of radius R has total surface area of 4pi*R^2 = 4pi*1.00 = 12.57 m^2
So 1 m^2 of this area is 1/12.57 = 0.08 of total surface, so flux thru 1 m^2 = 0.08*(Q/e0)
= 0.08*5e-6/8.85e-12 = 45,200 N-m^2/C answer is (b).
(The 20 cm is a red herring. It could be anything from 0+ cm to 100- cm.)
Shell of radius R has total surface area of 4pi*R^2 = 4pi*1.00 = 12.57 m^2
So 1 m^2 of this area is 1/12.57 = 0.08 of total surface, so flux thru 1 m^2 = 0.08*(Q/e0)
= 0.08*5e-6/8.85e-12 = 45,200 N-m^2/C answer is (b).
(The 20 cm is a red herring. It could be anything from 0+ cm to 100- cm.)