Consider a vector field A-r- The closed loop line integral -A-dl- can be expressed as

Electric field lines never form closed loops as they are conservative in nature. Explain how? What is the link between being conservative and not forming closed loops?

Q. The closed loop line integral

\oint_{| z | = 5} \frac{z^{3} + z^{2} + 8}{z + 2} d z

evaluated counterclockwise, is

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Consider a vector field →A(→r). The closed loop line integral ∮→A.d→l can be expressed as

The correct option is D ∬(∇×→A).→ds over the open surface bounded by the loopBy stoke's theorem ∮→A.d→l=∬(∇×→A).d→S (i.e closed loop line integral to open surface integral)

Consider a vector field $\to A (\to r)$ . The closed loop line integral $\oint \to A . d \to l$ can be expressed as

The correct option is D $\iint (\nabla \times \to A) . \to d s$ over the open surface bounded by the loop
By stoke's theorem
$\oint \to A . d \to l = \iint (\nabla \times \to A) . d \to S$
(i.e closed loop line integral to open surface integral)