GATE EE 2015 Set 2 — Question 13
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Electromagnetic Fields → Complex Variables → Cauchy's Integral Theorem
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Question
Match the following.
| P. Stokes's Theorem | 1. |
|---|---|
| Q. Gauss's Theorem | 2. |
| R. Divergence Theorem | 3. |
| S. Cauchy's Integral Theorem | 4. |
Correct answer
(B) P-4, Q-1, R-3, S-2
Solution
The matching is based on fundamental theorems in vector calculus and complex analysis:
1.Stokes's Theorem: Relates the surface integral of the curl of a vector field to the line integral of the field around the boundary. (P matches 4).
2.Gauss's Law (Theorem): In electrostatics, the flux of the electric displacement field through a closed surface is equal to the enclosed charge . (Q matches 1).
3.Divergence Theorem: Relates the volume integral of the divergence of a vector field to the surface integral of the field over the boundary. (R matches 3).
4.Cauchy's Integral Theorem: For an analytic function , the integral around a closed contour is zero. (S matches 2).
Thus, the correct matching is P-4, Q-1, R-3, S-2, which is option (B).Continue learning with Success Tracker
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