GATE EE 2020 Set 1 — Question 50
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Electromagnetic Fields → Electrostatics → Electric Flux & Gauss's Law
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Question
Let and be unit vectors along and directions, respectively in the cylindrical coordinate system. For the electric flux density given by Coulomb/m, the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:
Correct answer
(D) 180 π
Solution
According to Gauss's Divergence Theorem, the total electric flux emanating from a volume is given by:In cylindrical coordinates, the divergence of is:Given , we have:
The total flux is:
The total flux is:
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