A block of mass $m$ is suspended vertically with a spring of spring constant $k.$ The block is made to oscillate in a gravitation field. Its time period is found to be $T.$ Now the space between the plates is made gravity free and an electric field $E$ is produced in the downward direction. Now the block is given a charge $q.$ The new time period of oscillation is, 

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

If the electric potential of the inner shell is $10$ volt and that of the outer shell is $5$ volt, then the potential at the centre will be: (the shells are uniformly charged) 

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,