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:

Three point charges $q_1, q_2, q_3$ are placed at the vertices of a triangle. If the forces on $q_1$ and $q_2$ are $(2\hat{i} - \hat{j}) \, N$ and $(\hat{i} + 3\hat{j}) \, N$,respectively,then what will be the force on $q_3$?

An uncharged metal sphere is placed between two charged parallel plates. The pattern of the electric field lines will be:

Two identical charges $+Q$ are kept fixed at some distance apart. $A$ small particle $P$ with charge $q$ is placed midway between them. If $P$ is given a small displacement $\Delta$,it will undergo simple harmonic motion if:

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $\sigma'$,and a point charge $q_A$ is placed at the center of the shell,then choose the correct statement$(s)$.

Five balls numbered $1$ to $5$ are suspended using separate threads. Pairs $(1, 2), (2, 4)$ and $(4, 1)$ show electrostatic attraction,while pairs $(2, 3)$ and $(4, 5)$ show repulsion. Ball $1$ must be: