An air capacitor is made by using two flat plates, each with area a, separated by a distance d. then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between the, parallel to the plates and not touching either plate

Solution:

As per the question:

Area of the plates is given by 'A'

Separation distance between the plates is 'd'

Now, after insertion of the metal plate with same area 'A' and thickness, a < d

in between the plates, the capacitance of the capacitor changes.

The capacitance of the air capacitor (parallel plate) is generally given by:

where

C = Capacitor's capacitance

= Permittivity of the free space

Now, when the metal slab is inserted the distance is reduced to (d - a)

Thus

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