The equation of an electric field line in the $xy$-plane is given by ${x^2} + {y^2} = 1$. What is true for a particle with unit positive charge initially at rest at the point $(1, 0)$ in the $xy$-plane?

Two charged conducting spheres of radii $5 \ cm$ and $10 \ cm$ have equal surface charge densities. If the electric field on the surface of the smaller sphere is $E$,then the electric field on the surface of the larger sphere is

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:

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?

Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$ of side $a$. The magnitude of the electric field at point $C$ is:

Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ} .$ The electric field in the region shown between them is given by