You do use RHR for solenoid. It's just in a different kind of plane. When you're talking about a moving charge that feels a force due to a field, you use the RHR. When you're talking about the current creating a field like in a solenoid, it kind of curls around.
Use your thumb to point conventional current in the same direction as the arrows of the 2nd picture at the south side. Curl your fingers. Shift your hand over and realize it's the same for the north side! You're using the same rule. And yes, if it were wrapped the other way, I think it would be the opposite--you've just flipped the solenoid over, though.
Use your thumb to point conventional current in the same direction as the arrows of the 2nd picture at the south side. Curl your fingers. Shift your hand over and realize it's the same for the north side! You're using the same rule. And yes, if it were wrapped the other way, I think it would be the opposite--you've just flipped the solenoid over, though.