The work done in rotating a dipole placed parallel to the electric field through $180^{\circ}$ is $w$. What is the work done in rotating it through $60^{\circ}$? $(\cos 0^{\circ}=1, \cos 60^{\circ}=\frac{1}{2}, \cos 180^{\circ}=-1)$

Three point charges $Q$, $+2q$ and $+q$ are placed at the vertices of a right-angled isosceles triangle of side length $\sqrt{2}a$. The net electrostatic potential energy of the configuration is zero, if $Q$ is equal to

Three point charges of $2 \ mC$ each are kept at the vertices of an equilateral triangle of side $50 \ cm$. If the system is supplied energy at the rate of $2 \ kW$,the time taken to move one of the charges to the midpoint of the line joining the other two charges is (in $s$)

Three charges $-q, Q$ and $-q$ are placed respectively at equal distances on a straight line. If the potential energy of the system of three charges is zero,then what is the ratio of $Q: q$ ?

Two point charges $q_1 = 6 \mu\text{C}$ and $q_2 = 4 \mu\text{C}$ are kept at points $A$ and $B$ in air where distance $AB = 10 \text{cm}$. What is the increase in potential energy of the system when $q_2$ is moved towards $q_1$ by $2 \text{cm}$? $(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{SI units})$

Three infinitely long linear charges of charge density $\lambda$,$\lambda$,and $-2\lambda$ are placed in space. $A$ point in space is specified by its perpendicular distances $r_1$,$r_2$,and $r_3$ respectively from the linear charges. For the points which are equipotential: