Three concentric spheres with radii 3, 4 and 5 m have uniform surface charge densities 8, -12 and ${\rho }_s nC/m^2$ respectively. What should be value of ${\rho }_s$ so that net flux coming out of a Gaussian sphere with radius greater than 5 will be zero ?

Charge distribution inside a sphere of radius 10 is given as ${\rho }_v = 2 r nC/m^3$. Determine electric flux density $\overline{D}$ for a Gaussian spherical surface at r = 2.

Spherical surfaces at r=2 and r =4 carry uniform charge densities of $20 nC/m^2$ and $-4 nC/m^2$ respectively. The $\overline{D}$ at 2 < r < 4 can be expressed as _________ .

Gauss theorem uses which of the following operations?

Evaluate ${\oint }_s (3 x \overline{a_x}+ 2 y \overline{a_y}) · ds$ for a closed spherical surface defined by $x^2+y^2+z^2=9$.

Three coaxial cylindrical sheets are present in free space with radius 2, 4 and 6 m. Each surface has uniform surface charge densities of $2 nC/m^2$, $-4 nC/m^2$ and $6 nC/m^2$ respectively. Magnitude of electric flux density (in $nC/m^2$) for Gaussian cylindrical surface with r = 1.

Three coaxial cylindrical sheets are present in free space with radius 2, 4 and 6 m. Each surface has uniform surface charge densities of $2 nC/m^2$, $-4 nC/m^2$ and $6 nC/m^2$ respectively. Magnitude of electric flux density (in $nC/m^2$) for Gaussian cylindrical surface with 2< r <4 will be ________.

Three coaxial cylindrical sheets are present in free space with radius 2, 4 and 6 m. Each surface has uniform surface charge densities of $2 nC/m^2$, $-4 nC/m^2$ and $6 nC/m^2$ respectively. Magnitude of electric flux density (in $nC/m^2$) for Gaussian cylindrical surface with 4 < r < 6 will be ________.

With Gauss law as reference which of the following law can be derived?

Evaluate ${\oint }_s (3 r \overline{a_r}+ 2 z \overline{a_z}) · ds$ for a closed cylindrical surface with r = 2 m and 0 < z < 4 m.