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Question

A uniform electric field E=500 N/C passes through a hemispherical surface of radius R=1.2 m as shown in the figure. The net electric flux (in SI units) through the hemispherical surface only in Nπ. Find the value of N.



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Solution

To calculate flux, we always take the projectional surface area.
Projectional area of hemispherical surface of radius R would be a circle of area πR2
Also, the angle between electric field and area vector of circle is 370[900530=370]
ϕ=E.S=EScos370=E.πR2cos370



Given, E=500NC1,
R=1.2m,cos370=45
ϕ=500×π×(1.2)2×45
ϕ=576πNC1m2
Also, from question:
ϕ=NπNC1m2
N=576
Hence, the value of N is 576

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