A hollow sphere of charge does not produce an electric field at any

Electric field at centre $O$ of semicircle of radius $a$ having linear charge density $\lambda$ given is given by

Two point charges $q_1$ and $q_2 (=q_1/2)$ are placed at points $A(0, 1)$ and $B(1, 0)$ as shown in the figure. The electric field vector at point $P(1, 1)$ makes an angle $\theta $ with the $x-$ axis, then the angle $\theta$ is

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 .....$\mu C$

A charged ball $B$ hangs from a silk thread $S$, which makes an angle $\theta $ with a large charged conducting sheet $P$, as shown in the figure. The surface charge density $\sigma $ of the sheet is proportional to

For the given figure the direction of electric field at $A$ will be