The dimension of $\frac{1}{2} \varepsilon_0 E^2$ (where $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field) is:

$A$ particle of mass $2\,g$ and charge $1\,\mu C$ is released from a distance of $1\,m$ from a fixed charge of $1\,mC$. What will be the velocity of the particle at a distance of $10\,m$ from the fixed charge (in $m/s$)?

The diagram shows three infinitely long uniform line charges placed on the $X, Y$ and $Z$ axes with linear charge densities $2\lambda, 3\lambda$ and $\lambda$ respectively. The work done by an external agent in moving a unit positive charge from $(1, 1, 1)$ to $(0, 1, 1)$ is equal to:

An oil drop carries six electronic charges,has a mass of $1.6 \times 10^{-12} \text{ g}$ and falls with a terminal velocity in air. The magnitude of the vertical electric field required to make the drop move upward with the same speed as it was formerly moving is ........$kN/C$.

Given below are two statements:
Statement $I$: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero,but the electric field is not zero anywhere in the sphere.
Statement $II$: If $R$ is the radius of a solid metallic sphere and $Q$ is the total charge on it,the electric field at any point on a spherical surface of radius $r$ ( < R ) is zero,and the electric flux passing through this closed spherical surface of radius $r$ is also zero.
In the light of the above statements,choose the correct answer from the options given below:

Three charges are placed as shown in the figure. The magnitude of $q_1$ is $2.00\, \mu C$,but its sign and the value of the charge $q_2$ are not known. Charge $q_3$ is $+4.00\, \mu C$,and the net force on $q_3$ is entirely in the negative $x-$ direction. As per the condition given,the signs of $q_1$ and $q_2$ will be