The tiny ball at the end of the thread shown in the 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 particle of mass $m$ and charge $q$ is at rest. It is accelerated in a uniform electric field of intensity $E$ for time $t$. The kinetic energy of the particle after time $t$ is

The electric potential varies in space according to the relation $V = 3x + 4y$. $A$ particle of mass $0.1 \, kg$ starts from rest from point $(2, 3.2)$ under the influence of this field. The charge on the particle is $+1 \, \mu C$. Assume $V$ and $(x, y)$ are in $S.I.$ units. The time taken to cross the $x$-axis is.....$s$

The electric field intensity just sufficient to balance the earth's gravitational attraction on an electron will be: (Given: mass of an electron $m = 9.1 \times 10^{-31} \ kg$,charge of an electron $e = 1.6 \times 10^{-19} \ C$,and acceleration due to gravity $g = 10 \ m/s^2$.)

In a certain region,a uniform electric field $E$ and a magnetic field $B$ are present in opposite directions. At the instant $t = 0$,a particle of mass $m$ carrying a charge $q$ is given a velocity $v_0$ at an angle $\theta$ with the $y$-axis,in the $yz$-plane. The time after which the speed of the particle would be minimum is equal to

An electron of mass $m_e$ and a proton of mass $m_p$ are kept in a uniform electric field. The ratio of the acceleration of electron $(a_e)$ to the acceleration of proton $(a_p)$ is