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 $P$.

The tiny ball at the end of the thread shown in figure has a mass of $0.5 \, g$ and is  placed in a horizontal electric field of intensity $500\, N/C$. It is in equilibrium in the  position shown. The magnitude and sign of the charge on the ball is .....$\mu C$

The three charges $q / 2, q$ and $q / 2$ are placed at the corners $A , B$ and $C$ of a square of side ' $a$ ' as shown in figure. The magnitude of electric field $(E)$ at the comer $D$ of the square, is

For a uniformly charged ring of radius $R$, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then value of $h$ is

The distance between a proton and electron both having a charge $1.6 \times {10^{ - 19}}\,coulomb$, of a hydrogen atom is ${10^{ - 10}}\,metre$. The value of intensity of electric field produced on electron due to proton will be

Deutron and $\alpha - $ particle are put $1\,\mathop A\limits^o $ apart in air. Magnitude of intensity of electric field due to deutron at $\alpha - $ particle is