Question

In induction the charge induced in the near surface of a dielectric is
a. Equal and dissimilar
b. Greater and dissimilar
c. Lesser and dissimilar
d. Equal and similar

ans is c. How?

Answer 1

The key here is the term "dielectric". A dielectric does not conduct the charge carriers to where they are most comfortable. Instead, in a dielectric the electric field from a nearby charge causes polarization of the molecules -- meaning they orient themselves so they are more comfortable, but they stay in place. See sheet 54 here (*) and preceding slides. This orientation reduces the field strength, but doesn't bring it all the way down to zero. That corresponds to a net surface charge that is less than the inducing charge. As they say in the sheet: If the dielectric were replaced with a conductor, the net field between the plates would be zero zero because the surface charge is then equal to the induced charge. So the general answer to your question is yes, namely in case of a conductor. But for dielectriccs, which seems to be what the book statement is about, the induced charge is always smaller than the inducing charge. 

Answer 2

Answer :- In induction the charge induced in the near surface of a dielectric is Lesser and dissimilar .

The induced charge near surface of a dielectric is less than free charge and is dissimilar i.e. of opposite polarity.

q(p) = q ( 1 - 1/K )  here K - dielectric constant of dielectric

q(p) - Induced charge

q  - Free charge

So, q(p) is opposite sign of q.

Also q(p) will be less than q since q x (Number less than 1) will be less than q.