Find the force experienced by the semicircular rod charged with a charge $q$, placed as shown in figure. Radius of the wire is $R$ and the line of charge with linear charge density $\lambda $ is passing through its centre and perpendicular to the plane of wire.
$\frac{{\lambda q}}{{2{\pi ^2}{\varepsilon _0}R}}$
$\frac{{\lambda q}}{{{\pi ^2}{\varepsilon _0}R}}$
$\frac{{\lambda q}}{{4{\pi ^2}{\varepsilon _0}R}}$
$\frac{{\lambda q}}{{4\pi {\varepsilon _0}R}}$
The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius $R$ is $E.$ The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is
Two infinitely long parallel conducting plates having surface charge densities $ + \sigma $ and $ - \sigma $ respectively, are separated by a small distance. The medium between the plates is vacuum. If ${\varepsilon _0}$ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is
A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre, for $x < R$, the electric field is directly proportional to
Consider the force $F$ on a charge $'q'$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F,$ if $'q'$ is placed at distance $r$ from the centre of the shell $?$
A spherically symmetric charge distribution is considered with charge density varying as
$\rho(r)=\left\{\begin{array}{ll}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { Zero } & \text { for } r>R\end{array}\right.$
Where, $r ( r < R )$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be.