To determine the appropriate use of magnetic materials $A$ and $B$, we need to consider the characteristics of their hysteresis loops.
The hysteresis loop of a magnetic material provides information about its magnetic properties like coercivity, retentivity, and energy loss due to hysteresis.
Coercivity: It is the ability of a material to withstand an external magnetic field without becoming demagnetized.
Retentivity: It measures the ability of a material to retain a certain amount of magnetization after the external magnetic field is removed.
Energy Loss: It is proportional to the area enclosed by the hysteresis loop. Materials with a large loop area have higher energy loss, and vice versa.
For transformers and electromagnets, materials with low coercivity and low hysteresis loss are preferred to reduce energy loss. This typically means a narrow hysteresis loop.
For electric generators, materials need to have high coercivity to maintain magnetization under mechanical stress, usually indicated by a wide hysteresis loop.
From the given options, Material $B$ should be used for transformers and electromagnets due to its narrow hysteresis loop, indicating low energy loss, which is ideal for continuous operation.
Therefore, the correct answer is: $B$ for electromagnets and transformers.