The electric field at the centre $O$ of a semicircle of radius $a$ having a linear charge density $\lambda$ is given by:

Four charges are placed on the corners of a square as shown in the figure,with a side length of $5 \, cm$. If $Q = 1 \, \mu C$,then the electric field intensity at the centre will be:

Charges $Q_{1}$ and $Q_{2}$ are at points $A$ and $B$ of a right-angled triangle $OAB$ (see figure). If the resultant electric field at point $O$ is perpendicular to the hypotenuse $AB$,then $Q_{1} / Q_{2}$ is proportional to:

Two charged thin infinite plane sheets of uniform surface charge density $\sigma_{+}$ and $\sigma_{-}$ where $\left|\sigma_{+}\right|>\left|\sigma_{-}\right|$ intersect at a right angle. Which of the following best represents the electric field lines for this system?

$A$ spherical conductor of radius $10 \, cm$ has a charge of $3.2 \times 10^{-7} \, C$ distributed uniformly. What is the magnitude of the electric field at a point $15 \, cm$ from the centre of the sphere?
$\left(\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^{9} \, Nm^{2}/C^{2}\right)$

Five charges,each $q$,are placed at the corners of a regular pentagon of side $a$ as shown in the figure.
$(a)$ $(i)$ What will be the electric field at $O$,the centre of the pentagon?
$(ii)$ What will be the electric field at $O$ if the charge from one of the corners (say $A$) is removed?
$(iii)$ What will be the electric field at $O$ if the charge $q$ at $A$ is replaced by $-q$?
$(b)$ How would your answer to $(a)$ be affected if the pentagon is replaced by an $n$-sided regular polygon with charge $q$ at each of its corners?