A cube is placed inside an electric field, $\overrightarrow{{E}}=150\, {y}^{2}\, \hat{{j}}$. The side of the cube is $0.5 \,{m}$ and is placed in the field as shown in the given figure. The charge inside the cube is $.....\times 10^{-11} {C}$

If a spherical conductor comes out from the closed surface of the sphere then total flux emitted from the surface will be

A metallic shell has a point charge ‘$q$’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces

The total charge enclosed in an incremental volume of $2 \times 10^{-9} \,{m}^{3}$ located at the origin is ...... $nC,$ if electric flux density of its field is found as $D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k}\, C / m^{2}$

The figure shows two situations in which a Gaussian cube sits in an electric field. The arrows and values indicate the directions and magnitudes (in $N-m^2/C$) of the electric fields. What is the net charge (in the two situations) inside the cube?

$(a)$ An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?

$(b)$ Explain why two field lines never cross each other at any point?