Choose the incorrect statement:
(a) The electric lines of force entering into a Gaussian surface provide negative flux.
(b) A charge $q$ is placed at the centre of a cube. The flux through all the faces will be the same.
(c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
(d) When an electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.

Choose the most appropriate answer from the options given below:

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

A body having specific charge $8 \mathrm{\mu C} {\mathrm{g}}^{-1}$ is resting on a frictionless plane at a distance $10 \mathrm{cm}$ from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of $100 \mathrm{V} {\mathrm{m}}^{-1}$ is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be $\_\_\_\_\mathrm{s}.$

A parallel plate capacitor with plate area '$A$' and distance of separation '$d$' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as:

$\epsilon \left(x\right)={\epsilon }_0+kx$, for $\left(0<x\le \frac{d}{2}\right)$

$\epsilon \left(x\right)={\epsilon }_0+k\left(d-x\right)$, for $\left(\frac{d}{2}\le x\le d\right)$