A thin glass rod is bent into a semicircle of radius $r$. A charge $+Q$ is uniformly distributed along the upper half, and a charge $-Q$ is uniformly distributed along the lower half, as shown in figure. The electric field $E$ at $P$, the centre of the semicircle, is

Find the electric field vector at $P$ $\left(a,a,a\right)$ due to three infinitely long lines of charges along the $x$-, $y$- and $z$ – axes, respectively. The charge density, i.e., charge per unit length of each wire is $\lambda$

Two semicircular rings lying in same plane, of uniform linear charge density $\lambda$ have radius $r$ and $2r$. They are joined using two straight uniformly charged wires of linear charge density $\lambda$ and length $r$ as shown in figure. The magnitude of electric field at common centre of semi circular rings is

Two concentric uniformly charged spheres of radius $10 \mathrm{cm}$ and $20 \mathrm{cm}$ are arranged as shown in the figure. The potential difference between the spheres is, 

An electric dipole is placed in a uniform electric field $\overrightarrow{E}$ of magnitude $40 \mathrm{N} {\mathrm{C}}^{-1}$. The graph shows the magnitude of the torque on the dipole versus the angle $\mathrm{\theta }$ between the field $\overrightarrow{E}$ and the dipole moment $\overrightarrow{p}$. The magnitude of dipole moment $\overrightarrow{p}$ is equal to