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.....$s$

An electron enters an electric field of $9.1 \times 10^6 \ N/C$. The acceleration produced is ..... $m/s^2$.

$A$ stream of positively charged particles having $\frac{q}{m} = 2 \times 10^{11} \text{ C/kg}$ and velocity $\overrightarrow{v}_0 = 3 \times 10^7 \hat{i} \text{ m/s}$ is deflected by an electric field $1.8 \hat{j} \text{ kV/m}$. The electric field exists in a region of $10 \text{ cm}$ along the $x$-direction. Due to the electric field,the deflection of the charged particles in the $y$-direction is $........... \text{ mm}$.

$A$ $3 \text{ C}$ charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2\hat{i} + 3\hat{j} + 4\hat{k} \text{ N/C}$. The work done in moving the charge is . . . . . . $J$.

$A$ charged bead is sliding freely through a string held vertically under tension. An electric field is applied parallel to the string so that the bead stays at rest at the middle of the string. If the electric field is switched off momentarily and switched on again,then

An electron is rotating around an infinite positive linear charge in a circle of radius $0.1 \,m$. If the linear charge density is $1 \,\mu C/m$,then the velocity of the electron in $m/s$ will be ...... $\times 10^7$.