In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{\mathrm{i}}+4\hat{\mathrm{j}}+3\hat{\mathrm{k}}.$ The electric flux through a surface area of $100$ units in $x-y$ plane is,

Electric charge is uniformly distributed over a long straight wire of radius 1 mm. The charge per cm length of the wire is Q coulombs. A cylindrical surface of radius 50 cm and length 1m encloses the wire symmetrically as shown in fig.

The total flux passing through the cylindrical surface is:

Gauss law is given by ${\in }_0\oint \overrightarrow{E}.\overrightarrow{ds}=q,$ if net charge enclosed by Gaussian surface is zero then-.

The total flux associated with the given cube will be-where 'a' is side of the cube:

$\left(\frac{1}{\epsilon }=4\pi \times 9\times {10}^9 \mathrm{SI} \mathrm{units}\right)$

As shown in the fig. charges $+q$ and $-q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is: