GATE EC 1987 Electromagnetics Solution Q 1

GATE EC 1987 Electromagnetics Solution Q 1

An electrostatic field is said to be conservative when:

a) The divergence of the field is equal to zero

b) The curl of the field is equal to zero

c) The curl of the field is equal to -\frac{\partial E}{\partial t^2}

d) The Laplacian of the field is equal to \mu\varepsilon\frac{\partial^2E}{\partial t^2}

Ans- b

Explanation

An electrostatic field is said to be conservative when the closed line integral of the field is zero.

\oint\overrightarrow E\cdot\overrightarrow{dl}=0

According to the Stoke’s theorem

\oint\limits_C\overrightarrow E\cdot\overrightarrow{dl}=\int\limits_s\left(\nabla\times\overrightarrow E\right)\cdot\overrightarrow{ds} \nabla\times\overrightarrow E=0

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