“Can a body at rest make another body move,according to the laws of Newton this is impossible. The question is in magnetism, If it happens then why is it not predicted by classical mechanics?”
Answer: First of all I congratulate you for your genuine thought. It is the critical thinking which will lead you to great discoveries.
To answer your question, let me ask you the question – When an apple falls to earth, the earth is also attracted by the apple by an equal and opposite force, then why earth is not moving towards the apple?
The difference lies in the acceleration achieved. a= F/m
Since mass of earth is very much large, its acceleration towards apple is negligibly small compared to the acceleration due to gravity (9.8 m/s2)
When the magnet attracts another magnet or a magnetic substance, both are experiencing the same force. But it is common that we generally hold the magnet restricting its motion. Therefore, it is not able to move towards the other one.
Newton’s third law is valid and correct even if the forces are contact forces or non contact forces.