What is the ruling of Islamic law on a man undergoing a vasectomy without informing his second wife?

What you did by permanently preventing procreation is forbidden and impermissible. You should have inquired about its ruling before undertaking it, as Allah Almighty says: (So ask the people of the message if you do not know). This act is an infringement on the wife's right to procreate. The majority of jurists have stipulated the wife's permission for the permissibility of 'azl (coitus interruptus), because she has the right to procreate. Therefore, you must repent from this action and increase your good deeds.