Teaching electricity and magnetism is complicated by the challenge that the magnetic forces are perpendicular to the motion of the particles and currents. This requires a three-dimensional perspective which can introduce a variable of a "wrong" direction. To prevent errors, let us be "right" and use the right-hand rule. Some would claim that there is only one right-hand rule, but I have found the convention of three separate rules for the most common situations to be very convenient.
Physics - Electric Motor
Magnetic fields of currents
When using the Right-Hand Rules, it is important to remember that the rules assume charges move in a conventional current the hypthetical flow of positive charges. In order to apply either Right-Hand Rule to a moving negative charge, the velocity v of that charge must be reversed--to represent the analogous conventional current. Because the force exerted on a moving charge by a magnetic field is perpendicular to both the the velocity of the charge and the direction of the field, making illustrations of these interactions involves using the two symbols on the left to denote movement into or out of the plane of the page. Using your right-hand: point your index finger in the direction of the charge's velocity, v , recall conventional current. Point your middle finger in the direction of the magnetic field, B. Your thumb now points in the direction of the magnetic force, F magnetic. Using your right-hand: Curl your fingers into a half-circle around the wire, they point in the direction of the magnetic field, B Point your thumb in the direction of the conventional current.
Introduction to Vector Mathematics
The direction of angular quantities, such as angular velocity and angular momentum, is determined by using the right hand rule. Angular momentum and angular velocity have both magnitude and direction and, therefore, are vector quantities. The direction of these quantities is inherently difficult to track—a point on a rotating wheel is constantly rotating and changing direction. The axis of rotation of a rotating wheel is the only place that has a fixed direction. The direction of angular momentum and velocity can be determined along this axis.
Fleming's left-hand rule for electric motors is one of a pair of visual mnemonics , the other being Fleming's right-hand rule  for generators. They were originated by John Ambrose Fleming , in the late 19th century, as a simple way of working out the direction of motion in an electric motor , or the direction of electric current in an electric generator. When current flows through a conducting wire, and an external magnetic field is applied across that flow, the conducting wire experiences a force perpendicular both to that field and to the direction of the current flow i. A left hand can be held, as shown in the illustration, so as to represent three mutually orthogonal axes on the thumb, fore finger and middle finger.