What happens with the electric field between two capacitor?

consider the schematic, we have two capacitors, $$C_1$$ is charged and $$C_2$$ uncharged. (connect the plates together to keep the plates neutrally charged).

In principle $$C_1$$ generates an electric field $$E$$, but inside the plates of $$C_2$$ there is an electric field?

Another question, the electric field of C1 induces the charges in C2 to create an electric field of equal magnitude and in the opposite direction, then between the plates of C2 E = 0 because both E1 and E2 cancel, but that is assuming that E1 can go through C2, is this true?

No, there is no electric field inside the plates of $$C_2$$ because they have the same potential.
Notice that your statement on the plates being neutrally charged is wrong. When you connect the plates you put them at the same potential. In this case, the plates will be charged and the electric field they produce is of the same magnitude and opposite direction to the one produced by the plates of $$C_1$$.
• @ fra_pero I think there shouldn't be any charge on capacitor $C_1$ at all, as the conductor plates of $C_1$ completes the circuit, as we know there shouldn't be any charge accumulation on circuit by kirchoffs law , Hence no charge on $C_2$ plates – maverick May 10 '20 at 15:34
• @maverick I think the image is misleading, the plates of $C_1$ are not connected, otherwise the problem does not make any sense. Notice also the different colors (green, gray). – fra_pero May 10 '20 at 15:39
• @RicardoCasimiro This is true. However no assumption is made. Electromagnetism (at least at this elementary level) is linear; this means that the total electric field is the sum of all the electric fields. You simply have $E_1+E_2=0$ inside the plates of $C_2$. – fra_pero May 10 '20 at 16:41