GATE EE 2020 Set 1 — Question 43
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Electromagnetic Fields → Electrostatics → Dielectric Media
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Question
The static electric field inside a dielectric medium with relative permittivity, , expressed in cylindrical coordinate system is given by the following expressionwhere are unit vectors along and directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, , in SI units is given by:
Correct answer
(D) 9ε₀
Solution
According to Gauss's Law in differential form:
where .The electric field is given in cylindrical coordinates as:
The divergence in cylindrical coordinates is:
Substituting the components of :
Now, find the volume charge density :
Thus, the volume charge density is .
where .The electric field is given in cylindrical coordinates as:
The divergence in cylindrical coordinates is:
Substituting the components of :
Now, find the volume charge density :
Thus, the volume charge density is .
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