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Q.

The electric potential at a point (x, y, z) is given by :V=−x2y−xz3+4The electric field E→ at that point is :

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a

E→=i^2xy−z3+j^xy2+3z2xk^

b

E→=2xy+z3i^+x2j^+3xz2k^

c

E→=i^2xy+j^x2+y2+k^ 3xz−y2

d

Eȷ^=i^z3+j^xyz+k^z2

answer is B.

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Detailed Solution

V=−x2y−xz3+4Ex=−∂V∂x=−∂−x2y−xz3+4∂x=+2xy+z3Ey=−∂V∂y=−∂−x2y−xz3+4∂y=+x2Ez=−∂V∂z=−∂−x2y−xz3+4∂z=+3xz2so=E→=Exi^+Eyj^+Ezk^
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