Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1,2$ and $3$ of radii $R/2, R$ and $2 R$ respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres $1,2$ and $3$ are $E_1 E_2$ and $E_3$ respectively, then
$E_1 > E_2 > E_3$
$E_3 > E_1 > E_2$
$E_2 > E_1 > E_3$
$E_3 > E_2 > E_1$
Obtain Gauss’s law from Coulomb’s law.
Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ} .$ The electric field in the region shown between them is given by
A positive charge $q$ is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance $\vec l $ . Force on charge $q$ is :
A conducting sphere of radius $10 \;cm$ has an unknown charge. If the electric field $20\; cm$ from the centre of the sphere is $1.5 \times 10^{3} \;N / C$ and points radially inward, what is the net charge (in $n\;C$) on the sphere?
Mention applications of Gauss’s law.