The direction $\left(\mathrm{\theta }\right)$ of $\overrightarrow{E}$ at point $P$ due to uniformly charged finite rod will be

Find the force experienced by a semi-circular rod having a charge $q$ as shown in figure. Radius of the wire is $R$, and the line of charge with linear charge density $\lambda$ passes through its centre and is perpendicular to the plane of wire.

A large sheet carries uniform surface charge density $\sigma$. A rod of length $2l$ has a linear charge density $\lambda$ on one half and $-\lambda$ on the second half. The rod is hinged at the midpoint $O$ and makes an angle $\mathrm{\theta }$ with the normal to the sheet. The torque experienced by the rod 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