GATE EE 2025 Set 1 — Question 25
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Electromagnetic Fields → Electrostatics → Electric Flux & Gauss's Law
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Question
Which one of the following figures represents the radial electric field distribution caused by a spherical cloud of electrons with a volume charge density, for (both , are positive and is the radial distance) and for ?
Correct answer
(C) Fig. (iii)
Solution
Using Gauss's Law in spherical coordinates:
For :
This is a linear decrease from 0 at the center to at .For :
This represents a decay in the negative region.Comparing with the given figures, Fig. (iii) correctly represents this distribution.
For :
This is a linear decrease from 0 at the center to at .For :
This represents a decay in the negative region.Comparing with the given figures, Fig. (iii) correctly represents this distribution.
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