GATE EC 2014 Set 4 — Question 65
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Electromagnetics → Maxwell's Equations → Differential & Integral Forms
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Question
If is the electric field in a source free region, a valid expression for the electrostatic potential is
Correct answer
(D) 2xy³ - 3xyz²
Solution
The relationship between the electric field and the electrostatic potential is given by .Given the electric field , we can identify the components:
Integrating with respect to :
Now, differentiate this expression for with respect to and compare with :
Next, differentiate with respect to and compare with :
Since the partial derivatives of are zero, is a constant. Therefore, a valid expression for the potential is:
This matches option (D).
Integrating with respect to :
Now, differentiate this expression for with respect to and compare with :
Next, differentiate with respect to and compare with :
Since the partial derivatives of are zero, is a constant. Therefore, a valid expression for the potential is:
This matches option (D).
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