Right Hand Rule for Solenoids

The direction of the field inside the solenoid is a bit tricky to figure out. As shown in Figure (1), up near the wires and in between the turns, the field goes in a circle around the wire just as it does for a straight wire. As we go out from the wire the circular patterns merge to create the uniform field in the center of the solenoid.
We see, from Figure (1), that if the current goes around the coil in such a way that the current is up out of the paper on the right side and down into the paper on the left, then the field close to the wires will go in counterclockwise circles on the right and clockwise circles on the left. For both these sets of circles, the field inside the coil points down. As a result the uniform field inside the coil is down as shown.
There is a simple way to remember this result without having to look at the field close to the wires. Curl the fingers of your right hand in the direction of the flow of the current i in the solenoid, and your thumb will point in the direction of the magnetic field inside the soled noid. We will call this the right hand rule for solenoids.

Figure 1: If you know the direction of the current in the wire, you can determine the direction of the magnetic field by looking very close to the wire where the field goes around the wire. You get the same answer if you curl the fingers of your right hand around in the direction the current in the coil is flowing. Your thumb then points in the direction of the field.