In a region of space, suppose there exists a uniform electric field $\vec{E}=10 i\left(\frac{ v }{ m }\right)$. If a positive charge moves with a velocity $\vec{v}=-2 \hat{j}$, its potential energy

A simple pendulum with a bob of mass $m = 1\ kg$ , charge $q = 5\mu C$ and string length $l = 1\ m$ is given a horizontal velocity $u$ in a uniform electric field $E = 2 × 10^6\ V/m$ at its bottom most point $A$ , as shown in figure. It is given a speed $u$ such that the particle leave the circular path at its topmost point $C$ . Find the speed $u$ . (Take $g = 10\ m/s^2$ )

Mass of charge $Q$ is $m$ and mass of charge $2Q$ is $4\,m$ . If both are released from rest, then what will be $K.E.$ of $Q$ at infinite separation

Assertion : Electric potential and electric potential energy are different quantities.

Reason : For a system of positive test charge and point charge electric potential energy $=$ electric potential.

There exists an electric field of magnitude $E$ in $x$-direction. If the work done in moving a charge of $0.2 \,C$ through a distance of $2 \,m$ along a line making an angle $60^{\circ}$ with $x$-axis is $4 \,J$, then the value of $E$ is ........ $N / C$

A small sphere of mass $m =\ 0.5\, kg$ carrying a positive charge $q = 110\  \mu C$ is connected with a light, flexible and inextensible string of length $r = 60 \ cm$ and whirled in a vertical circle. If a vertically upwards electric field of strength $E = 10^5 NC^{-1}$ exists in the space, The minimum velocity of  sphere required at highest point so that it may just complete the circle........$m/s$  $(g = 10\, ms^{-2})$