# WHY: Why should we use left-fist rule?

• The thumb is in the fist which is more lively to some situation. (More in HOW section)
• I do not want to put down my pen when I am thinking and writing. (Sorry for the left-handed)

# WHAT: What is the left-fist rule?

1. Raise your left hand with thumb in your palm
2. Point your rest four fingers to $x$ OR one of the radius direction
3. Find a way so that you could scroll your fingers to $y$ direction to form a fist OR along the spin direction
4. the direction of your thumb is $z$ direction

# HOW: How to apply the left-fist rule?

• X-Y-Z direction: point fingers to $x$, find a way scroll to $y$, your thumb in your fist is pointing at $z$
• Cross Product $\vec{A} \times \vec{B}$: pointing four fingers to the direction of $\vec{A}$ with thumb in the palm, then curling four finger to the direction of $\vec{B}$, thumb in the fist is the direction of $\vec{A} \times \vec{B}$
• Torque direction: point fingers to the radius $R$, scroll with the force direction $F$, your thumb in your fist is pointing at the torque direction.
• Ampere’s Law
  • The given condition is a straight line of current/magnetic field: point your thumb in your fist to the line’s direction, the scrolling direction of your four fingers is the magnetic field/current direction.
  • The given condition is a loop of current/magnetic field: scroll your four fingers along the direction of the loop, the pointing direction of thumb is the direction of magnetic field/current.
• Motion in the magnetic field: scroll from $v$(Motion of the positive electron, not current and negative electron!) to $B$(in the magnetic field), thumb is the direction of $F/I$