The electric field in a region is radially outward and at a point is given by $E=250 \,r V / m$ (where $r$ is the distance of the point from origin). Calculate the charge contained in a sphere of radius $20 \,cm$ centred at the origin ......... $C$
$2.22 \times 10^{-6}$
$2.22 \times 10^{-8}$
$2.22 \times 10^{-10}$
$0$
A uniformly charged rod of length $4\,m$ and linear charge density $\lambda = 30\,\mu C/m$ is placed as shown in figure. Calculate the $x-$ component of electric field at point $P$.
Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero
Two beads, each with charge $q$ and mass $m$, are on a horizontal, frictionless, non-conducting, circular hoop of radius $R$. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ $\varepsilon_0$ is the permittivity of free space.]
Charges $Q _{1}$ and $Q _{2}$ arc at points $A$ and $B$ of a right angle triangle $OAB$ (see figure). The resultant electric field at point $O$ is perpendicular to the hypotenuse, then $Q _{1} / Q _{2}$ is proportional to
$ABC$ is an equilateral triangle. Charges $ + \,q$ are placed at each corner. The electric intensity at $O$ will be