In the shown arrangement, mass of $A =1 kg$, mass of $B = 2 kg$. Coefficient of friction between A and $B = 0.2.$

There is no friction between B and ground. The frictional force exerted by A on B equals 

Block A moves due to friction. Maximum acceleration of A can be $\frac{f_{max}}{m}$ or $\frac{\mu mg}{m}$ or $\mu g=0.2\times 10=2 m/s^2$. If both the blocks move together, then combined acceleration of A and B can be $\frac{10}{3}$ of $3.33 m/s^2$. Since, this is more than the maximum acceleration of A. Slipping between them will take place and force of friction will be maximum or $\mu m_{A}g=2N$.