Physics, Chemistry, Mathematics Forums

The Charge WILL NOT be zero. That is because, due to the earthing, the POTENTIAL of that plate will be zero.

 Note that only when there is no external electric field will the charge be zero for the potential to be zero. 

 Here, we have an external field, i.e. due to the charged isolated plate. 

 To solve this, we can use a trick, that the circuit may be created while keeping the system in its initial eqb state ( Note that here, there is no need to consider eqb for the ground plate coz its charge is unknown- however, since the other plate is in eqb, this too must be in eqb). Thus we may consider the two plates to be forming a capacitor.

 Thus we can connect a battery of emf = E = Q/C (C=AEo/d) to the two plates, keeping the lower potential as zero and the upper potential causing an accumulation of the charge Q on the other plate. Thus, we have created a circuit without disturbing the system.   

                                     (Charge=Q)

                  V=0     ---------| |----------V= +E

        Hence proceeding, the problem may be solved.

 Solving, we get charge as -Q, assuming both plates are of identical geometries.

NOTE:  In this case, the problem may be solved conveniently and quickly by the use of Gauss' Law, taking a small piece on the earthed plate and considering that Field, E= 0, since V=0 ( Note that the reverse doesnt hold true and that if E=0, then V= constant, not neccesserily zero). 

 However , this is a useful method for more complex cases.  

Skanda Prasad P.N.