how we can recognize that both the charges have either +ve or -ve charge
When we bring an alpha particle near the charge B and if the force of alpha particles on charge B is towards westwards and whereas the force on alpha particle by the charge B is eastwards then we can say that the charges have positively charge.
and when we bring the Beta particles towards a charge A charge and direction of force is same as we discuss above then we can say that both the charge are negatively charge.
When we bring together the two charges and if we see the attraction between them then we can say from coulomb's law that both the charges have different charges i.e. negatively charge and positively charge. And when we bring the two charges together and if we see repulsion between them then we can say from coulomb's law that both the charges have equal charge, i.e. may be positive charge or negative charge.