A point charge $+Q$ is placed at the centroid of an equilateral triangle. When a second charge $+Q$ is placed at a vertex of the triangle, the magnitude of the electrostatic force on the central charge is $8 \mathrm{N}$. The magnitude of the net force on the central charge when a third charge $+Q$ is placed at another vertex of the triangle is

A positively charged particle $P$ enters the region between two parallel plates with a velocity $u$, in a direction parallel to the plates. There is a uniform electric field in this region. $P$ emerges from this region with a velocity $v$.

Taking $C$ as a constant, $v$ will depend on $u$ as

A conducting spherical shell is earthed. A positive charge $+q_1$ is placed at the centre and another small positive charge $+q_2$ is placed at a distance $r$ from $q_1$ (see figure). Ignore the effect of induced charge due to the $q_2$ on the sphere. Then the Coulomb force on $q_2$ is

A conducting spherical shell is neutral. A positive charge $+q_1$ is placed at the centre and another small positive charge $+q_2$ is placed at a distance $r$ from $q_1$ (see figure). Ignore the effect of induced charge due to $q_2$ on the sphere. The force on $q_2$ is

An electric dipole consists of charges $\pm 2.0\times {10}^{-8} \mathrm{C}$ separated by a distance of $\pm 2.0\times {10}^{-3} \mathrm{m}$. It is placed at a distance of $6 \mathrm{c}\mathrm{m}$ from a line charge of linear charge density $4.0\times {10}^{-4} \mathrm{C} {\mathrm{m}}^{-1}$ as shown in the figure such that the dipole makes an angle of $\theta =60°$ with line $AB$. Find the force acting on the dipole.