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
${\tan ^{ - 1}}\left( {\frac{1}{2}} \right)$
${\tan ^{ - 1}}\left( {\frac{1}{4}} \right)$
${\tan ^{ - 1}}\left( 1 \right)$
${\tan ^{ - 1}}\left( 0 \right)$
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 tiny $0.50\, gm$ ball carries a charge of magnitude $10\, \mu C$. It is suspended by a thread in a downward electric field of intensity $300\, N/C$. If the charge on the ball is positive, then the tension in the string is
Write equation of electric field by system of $\mathrm{'n'}$ charges.
The intensity of the electric field required to keep a water drop of radius ${10^{ - 5}}\, cm$ just suspended in air when charged with one electron is approximately
Three charged particle $A, B$ and $C$ with charges $-4 q, 2 q$ and $-2 q$ are present on the circumference of a circle of radius $d$. the charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown in figure. Electric field at $O$ along $x-$direction is