If three infinite charged sheets of uniform surface charge densities $\mathrm{\sigma }, 2\mathrm{\sigma } \mathrm{and} –4\mathrm{\sigma }$ are placed as shown in figure, then find out electric field intensities at points $\mathrm{A}, \mathrm{B}, \mathrm{C} \mathrm{and} \mathrm{D}.$

 

A thread carrying a uniform charge $\lambda$ per unit length has the configurations shown in the figures $a$ and $b$. Assuming the curvature radius $R$ to be considerably less than the length of the thread, find the magnitude of the electric field strength at the point $O$.

A point charge $20 \mathrm{\mu C}$ is shifted from infinity to a point $P$ in an electric field with zero acceleration. If the potential of that point is $1000 \mathrm{volt}$, then

$\left(\mathrm{i}\right)$ Find out work done by an external agent against the electric field?

$\left(\mathrm{ii}\right)$ What is the work done by the electric field?

$\left(\mathrm{iii}\right)$ If the kinetic energy of the charged particle is found to increase by $10 \mathrm{mJ}$ when it is brought from infinity to point $P$, then what is the total work done by an external agent?

$\left(\mathrm{iv}\right)$ What is the work done by the electric field in the part $\left(\mathrm{iii}\right)$.

$\left(\mathrm{v}\right)$ If a point charge $30 \mathrm{\mu C}$ is released at rest at a point $P$, then find out its kinetic energy at a large distance?

Six equal point charges $q_0,$ each are placed at six corners of a regular hexagon of side $a$. Find out work required to take a point charge $q$ slowly. From infinity to the centre of hexagon.

A positive charge $Q=50 \mathrm{\mu C}$ is located in the $xy$ plane at a point having position vector $\stackrel{\rightharpoonup }{r_0}=\left(2\stackrel{⏜}{\mathrm{i}}+3\hat{\mathrm{j}}\right) \mathrm{m}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are unit vectors in the positive directions of $X$ and $Y$ axis, respectively. Find:

$\left(\mathrm{a}\right)$ The electric intensity vector and its magnitude at a point having coordinates $\left(8 \mathrm{m}, -5 \mathrm{m}\right)$.

Four charges $+q$, $+q$, $-q$ and $-q$ are fixed respectively at the corners of $A$, $B$, $C$ and $D$ of a square of side $a$ arranged in the given order. Calculate the electric potential and intensity at $O$ (Centre of the square). If $E$ and $F$ are the midpoints of sides $BC$, $CD$, respectively, what will be the work done by an external agent in carrying a charge $Q$ slowly from $O$ to $E$ and from $O$ to $F$?