Positive charge $$Q$$ is distributed uniformly over a circular ring of radius $$R$$. A point particle having a mass $$(m)$$ and a negative charge $$-q$$ is placed on its axis at a distance $$x$$ from the centre. Assuming $$x < R$$, find the time period of oscillation of the particle, if it is released from there [neglect gravity].

Assertion Mass of a body decreases slightly when it is negatively charged.

Reason Charging is due to transfer of electrons.

Charges $$+q$$ and $$-q$$ are placed at points $$A$$ and $$B$$ respectively which are a distance $$2 L$$ apart, $$C$$ is the mid-point between $$A$$ and $$B$$. The work done in moving a charge $$+Q$$ along the semicircle $$C R D$$ is

Assertion : The electric field due to a dipole on its axis line at a distance $$r$$ is $$E$$. Then, electric field due to the same dipole on the equatorial line and at the same distance will be $$E / 2$$.

Reason : Electric field due to dipole varies inversely as the square of the distance.