Two blocks a and b ($m_a> m_b$) are pushed for a certain distance along a frictionless surface. how does the magnitude of the work that a does on b compare to the magnitude of the work that b does on a?

the magnitude of the work done by the two blocks is the same.

Explanation:

The work done by block a on block b is given by:

where Fa is the force exerted by block a on block b, and d is the distance they cover.

The work done by block b on block a is given by:

where Fb is the force exerted by block b on block a, and d is still the distance they cover.

For Newton's third law, the force exerted by block a on block b is equal to the force exerted by block b on block a, therefore

and so

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it