Classification of Vector Fields and Important Vector Identities

Q. If the electric field intensity is given by
$\overrightarrow{E}=(x{\hat{u}}_x+y{\hat{u}}_y+z{\hat{u}}_z)$ Volt/m the potential difference between X(2, 0, 0) and Y(1, 2, 3) is

1. +1 volt
2. -1 volt
3. +5 volt
4. +6 volt

Q. Given the potential function in free space to be $V\left(x\right)=(50x^2+50y^2+50z^2)$ volts, the magnitude (in volts/metre) and the direction of the electric field at a point (1, -1, 1), where the dimensions are in meters, are

1. $100;(\hat{i}+\hat{j}+\hat{k})$
   
2. $\frac{100}{\sqrt{3}};(\hat{i}-\hat{j}+\hat{k})$
   
3. $100\sqrt{3}$; $(\hat{i}+\hat{j}-\hat{k})/\sqrt{3}$
   
4. $100\sqrt{3}$; $(-\hat{i}+\hat{j}-\hat{k})/\sqrt{3}$
   

Q. The line integral of the vector potential A around the boundary of a surface S represents

1. flux through the surface S
2. flux density in the surface S
3. magnetic density
4. current density