Three-point charges $q$ are placed at three corners of a square of side$a$ . Find out electric field intensity at the fourth corner of the square.

Two point charges $3\mathrm{\mu C} \mathrm{and} 2.5\mathrm{\mu C}$ are placed at point $\mathrm{A} (1,1,2)\mathrm{m} \mathrm{and} \mathrm{B} (0,3,–1)\mathrm{m}$ respectively. Find out electric field intensity at point $\mathrm{C}(3, 3, 3)\mathrm{m}.$

$\left(\mathrm{i}\right)$ Two infinitely long line charges each of linear charge density $\lambda$ are placed at an angle $\theta$ as shown in figure. Find out electric field intensity at a point $P$, which is at a distance $x$ from point $O$ along angle bisector of line charges. 

$\left(\mathrm{ii}\right)$ Repeat the above question if the line charge densities are $\mathrm{\lambda }$ and  $-\mathrm{\lambda }$as shown in figure.

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 $\mathrm{A}, \mathrm{B}, \mathrm{C} \mathrm{and} \mathrm{D}.$

Find out electric field intensity due to uniformly charged solid non-conducting sphere of volume charge density $\rho$ and radius $R$ at following points:

(i) at a distance $r$ from the surface of a sphere(inside),

(ii) at a distance $r$, from the surface of a sphere(outside),

Find out electric field intensity if the sphere is a hollow non-conducting sphere of volume charge density $\rho$ and radius $R$ at the following points, 

(i) at a distance $r$ from the surface of a sphere(inside),

(ii) at a distance $r$, from the surface of a sphere(outside),

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 $O$.