$A$ long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like the figure given in:

Answer carefully:
$(a)$ Two large conducting spheres carrying charges $Q_{1}$ and $Q_{2}$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by $Q_{1} Q_{2} / 4 \pi \varepsilon_{0} r^{2}$,where $r$ is the distance between their centres?
$(b)$ If Coulomb's law involved $1/r^{3}$ dependence (instead of $1/r^{2}$),would Gauss's law be still true?
$(c)$ $A$ small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
$(d)$ What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
$(e)$ We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
$(f)$ What meaning would you give to the capacitance of a single conductor?
$(g)$ Guess a possible reason why water has a much greater dielectric constant $(=80)$ than,say,mica $(=6)$?

Two equal negative charges $-q$ are placed at points $(0, a)$ and $(0, -a)$ on the $Y$-axis. A positive charge $q$ is released from rest at point $(2a, 0)$. What will be the motion of this charge?

Given below are two statements:
Statement-$I$: $A$ point charge is brought into an electric field. The value of the electric field at a point near the charge may increase if the charge is positive.
Statement-$II$: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.
Choose the correct answer from the options given below:

Consider two point charges of equal magnitude and opposite sign separated by a certain distance. The neutral point due to them

An inclined plane making an angle $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field of $100 \ Vm^{-1}$ as shown in the figure. $A$ small block of mass $1 \ kg$ and charge $0.01 \ C$ is allowed to slide down from rest from a height $h=1 \ m$. If the coefficient of friction is $0.2$,then the acceleration of the block is nearly,
(Acceleration due to gravity,$g=10 \ ms^{-2}$) (in $ms^{-2}$)