The distance between two charges $25\,\mu C$ and $36\,\mu C$ is $11\,cm$. At what point on the line joining the two charges will the electric field intensity be zero?

An infinite number of electric charges,each with a magnitude of $5 \, nC$,are placed along the $X$-axis at $x = 1 \, cm$,$x = 2 \, cm$,$x = 4 \, cm$,$x = 8 \, cm$,and so on. If the consecutive charges have opposite signs,find the electric field in $N/C$ at $x = 0$. (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \, N \cdot m^2/C^2$)

Four equal charges of value $+Q$ are placed at four vertices of a regular hexagon of side $a$. By suitably choosing the vertices,what can be the maximum possible magnitude of the electric field at the centre of the hexagon?

In the figure shown,the distance from point $A$ to the point where the electric field intensity is zero is .......... $cm$.

$A$ thin glass rod is bent in a semicircle of radius $R$. $A$ charge is non-uniformly distributed along the rod with a linear charge density $\lambda = \lambda_0 \sin \theta$ (where $\lambda_0$ is a positive constant and $\theta$ is the angle with the $x$-axis). The electric field at the centre $P$ of the semicircle is,

$A$ solid sphere of radius $R$ carries a positive charge $Q$ distributed uniformly throughout its volume. $A$ very thin hole is drilled through its center. $A$ particle of mass $m$ and charge $-q$ performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is