Physics:
The Right Hand Rule, illustrated at left, simply shows how a current-carrying wire generates a magnetic field. If you point your thumb in the direction of the current, as shown, and let your fingers assume a curved position, the magnetic field circling around those wires flows in the direction in which your four fingers point.
The Left Hand Rule shows what happens when charged particles (such as electrons in a current) enter a magnetic field. You need to contort your hand in an unnatural position for this rule, illustrated below. As you can see, if your index finger points in the direction of a magnetic field, and your middle finger, at a 90 degree angle to your index, points in the direction of the charged particle (as in an electrical current), then your extended thumb (forming an L with your index) points in the direction of the force exerted upon that particle. This rule is also called Fleming's Left Hand Rule, after English electronics pioneer John Ambrose Fleming, who came up with it.