Magnetic Field and Magnetic Forces

  • Magnetic forces: \vec{F}=q\vec{v}\times\vec{B}.
  • Gauss’s law for magnetism: \oint\vec{B}\cdot d\vec{A}=0.
  • Magnetic force on a conductor: d\vec{F}=Id\vec{l}\times\vec{B}.
  • Magnetic torque: \vec{\tau}=\vec{\mu}\times\vec{B}, \vec{\mu}=I\vec{A}.  U=-\vec{\mu}\cdot\vec{B}.
  • Magnetic field of a moving charge: \vec{B}=\frac{\mu_0}{4\pi}\frac{q\vec{v}\times\hat{\vec{r}}}{r^2}.
  • The law of Biot and Savart: d\vec{B}=\frac{\mu_0}{4\pi}\frac{Id\vec{l}\times\hat{\vec{r}}}{r^2}.
  • Magnetic field of a long, straight, current-carrying conductors: \vec{B}=\frac{\mu_0 I}{2\pi r}.
  • Magnetic force between two long, parallel, current-carrying conductors: \frac{F}{L}=\frac{\mu_0 I I\prime}{2\pi r}.
  • Magnetic field at the center of a current loop: B=\frac{\mu_0 I}{2r}.
  • Long solenoid that has n turns per unit length: B=\mu_0 n I.
  • Ampere’s law: \oint\vec{B}\cdot d\vec{l}=\mu_0 I_{encl}.
Advertisements

Neglecting Development of Your Pieces

Always start by playing out a center pawn, as this creates a line for developing a bishop.  Bring out the king knight very early – preferably to f3(f6).  By playing out the king knight and king bishop quickly, you make early castling possible and thus get your king out of any immediate danger.

Try to avoid placing your bishops on diagonals where they are blocked by your own pawns. Avoid, too, an excessive number of pawn moves – they contribute little or nothing to development.

Play over your games to see whether you are achieving the following minimum in the first ten moves: both center pawns advanced; both knights developed; both bishops developed; castling completed. This is an ideal goal which you may not always achieve, but it will help you to guard against moving the same piece repeatedly.

Managing the queen is a different matter. If you develop her too soon you will only expose her to harrying by enemy pieces of lesser value.

Reinfeld, Fred. “The Complete Chess Course: From Beginning to Winning Chess!”