"Induced force"? I think you mean applied force.
The direction of the current at any moment, in an AC generator is found by using the right hand rule. If you look in your physics textbook, or search google you'll find plenty of examples & diagrams of the right hand rule.
To answer your question "why", it is because this is the nature of vector cross products. To cross multiply two vectors, you use the right hand rule. Working out the magnitude and direction of the current involves finding the vector cross product of the magnetic field and the applied force. You don't really need to worry about cross products in detail at HSC level Physics though