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Basics [Coordinate Systems/Vector Calculus]
Q.1 An electrostatic potential is given by 
Ans:-
Explaination: – Electrostatic potential,
![\therefore\overrightarrow E\;=-\left[{\widehat a}_x\;\frac\partial{\partial x}\;\left(2x\sqrt y\;\right)+{\widehat a}_y\;\frac\partial{\partial y}\;\left(2x\sqrt y\;\right)\right]\;](http://s0.wp.com/latex.php?latex=%5Ctherefore%5Coverrightarrow+E%5C%3B%3D-%5Cleft%5B%7B%5Cwidehat+a%7D_x%5C%3B%5Cfrac%5Cpartial%7B%5Cpartial+x%7D%5C%3B%5Cleft%282x%5Csqrt+y%5C%3B%5Cright%29%2B%7B%5Cwidehat+a%7D_y%5C%3B%5Cfrac%5Cpartial%7B%5Cpartial+y%7D%5C%3B%5Cleft%282x%5Csqrt+y%5C%3B%5Cright%29%5Cright%5D%5C%3B&bg=ffffff&fg=000&s=0 "\therefore\overrightarrow E\;=-\left[{\widehat a}_x\;\frac\partial{\partial x}\;\left(2x\sqrt y\;\right)+{\widehat a}_y\;\frac\partial{\partial y}\;\left(2x\sqrt y\;\right)\right]\;")
Now, at x = 1 m and y = 1 m
Q.2 Given a vector field 
(a)
(b)
(c)
(d)
Ans:- (a)
Explanation:- The Divergence Theorem is applicable to the closed surface. It is simply remembered as, the surface integration of the vector field over the closed surface can also be calculated by taking the volume integration of the divergence of that vector field.