A block of mass $m$ containing a net negative charge $-q$ is placed on a frictionless horizontal table and is connected to a wall through an unstretched spring of spring constant $k$ as shown. If horizontal electric field $E$ parallel to the spring is switched on, then the maximum compression of the spring is :-
$ \sqrt {qE / k}$
$ \sqrt {k / qE}$
$qE/k$
$\frac{2qE}{k}$
Three charges $Q,( + q)$ and $( + q)$ are placed at the vertices of an equilateral triangle of side l as shown in the figure. If the net electrostatic energy of the system is zero, then $Q$ is equal to
A bullet of mass $m$ and charge $q$ is fired towards a solid uniformly charged sphere of radius $R$ and total charge $+ q$. If it strikes the surface of sphere with speed $u$, find the minimum speed $u$ so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)
The figure shows a family of parallel equipotential surfaces and four paths along which an electron is made to move from one surface to another as shown in the figur
$(I)$ What is the direction of the electric field ?
$(II)$ Rank the paths according to magnitude of work done, greatest first
Two points $P$ and $Q$ are maintained at the potentials of $10\, V$ and $-4\,V$, respectively. The work done in moving $100$ electrons from $P$ and $Q$ is