Two identical electric point dipoles have dipole moments $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$ and are held on the x axis at distance '$$a$$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is :

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?

Charges Q₁ and Q₂ are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then
$${{{Q_1}} \over {{Q_2}}}$$ is proportional to :

Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively.
(Take V = 0 at infinity)