E = U/d
where E is the electric field, U the voltage on the capacitor, d is the distance between plates.
1) If choice B, then U = constant, means E changes with d from above relation.
2)if choice C) then $U(t) = U(0)*exp(-t/RC)$ varies with time, then E also varies with time and with d from relation above.
3) A wire is equivalent to a zero resistance. See discussion from point 2) above. The charge on C will be zero, therefore U is zero, therefore E is zero.False choice since E is non zero specified.
4). Two capacitors are connected in parallel. Varying the external capacitance, the total charge will remain constant, thus the common voltage drop (the same for both C) will change. Thus E will change with d and with U from above relation.
The only choice remaining is A) the black box contains nothing. Explanation: (the capacitor energy)/(unit of volume) is remaining constant. $C/Volume = epsilon*E^2/2$.
Thus E is constant.