202401301506 Solution to 2000-CE-PHY-II-28

Two insulated uncharged metal spheres X and Y are placed in contact. A positively-charged rod is brought near X as shown below. X is then earthed momentarily. The charged rod is removed and the two spheres are then separated. Describe the charges on X and Y. (modified)


Roughwork.

Have some mental pictures (*make drawings if you don’t have ample RAM).

First, when a positively-charged rod is brought near X, charges are induced:

Notice that on surface areas X and Y making contact, as boxed below:

the net charge is zero, Q=0. Hence, the plus and the minus signs (representing positive and negative charges) are erased from the drawing:

Then, X is earthed momentarily:

it is convenient to treat the two spheres X and Y as one body X+Y:

The process of earthing enables a transfer of negative free charges (electrons being the carrier) unidirectionally between two bodies:

here from the earth to the body, but no reversed (why?); the plus and minus signs, as boxed below:

should cancel off each other, and are thus erased from the drawing:

once the charged rod is removed:

the negative charges will be redistributed over X+Y such that the electrostatic repulsive forces between them are kept to a minimum:

after the two spheres are separated,

both spheres X and Y will be negative charged. The descriptions go complete.


This problem is not to be attempted.