$\oint \overline{E}·\overline{dl} =0$ is indicative of

The expression $\oint \overline{E}·\overline{dl}$ is equivalent to which of the following expressions in point form.

Which of the following is true for the work done on a charge in a electric field. i) work done is independent of the path followed ii) work done in moving charge over a closed path is zero iii) if work done is negative it indicates that work is done by the field

Work done in moving a charge of $-2 \mu C$ from (2,1,-1) to (8,2,-1) along a path $x=2y^2$ in the electric field with $\overline{E} = y \overline{a_x} + x \overline{a_y}$ will be __________ $\mu J$.

Work done in moving a charge of $-2 \mu C$ from M(2,1,-1) to N(8,2,-1) along the straight line joining M and N in the electric field with $\overline{E} = y \overline{a_x} + x \overline{a_y}$ will be __________ $\mu J$.

If $\overline{E} = 4x \overline{a_x} + 2 \overline{a_y}$ V/m, find work done in moving unit positive charge along the curve xy=4 from (2,2,0) to (4,1,0).

Given that $\overline{E} = y \overline{a_x} + 2xz \overline{a_z}$ V/m. The work done in moving -4C charge from (2,-4,1) to (-1,3,2) will be ____.

If $\overline{E} = 10r\sin \theta \overline{a_r} +5r\cos \theta \overline{a_{\theta }}$ V/m, work done in moving -2C of charge from $A(5,30°,0°)$ to $B(10,90°,60°)$ will be ____________ .

If $V = x{y}^2(z+4)$ V, then $\overline{\mathrm{E}}$ at point (1,2,-3) will be ________.

Two point charge $-4 \mu C$ and $5 \mu C$ are located at (2,-1,3) and (0,4,-2) respectively. Assuming zero potential at infinity the potential at (1,0,1) will be ____________.