Magnetic Field Lines

Magnetic field lines show both the direction and magnitude of the magnetic field B(x,y,z). At every point in space, the direction of the field lines is the direction of B, while the density of the lines shows the magnitude of B — the denser the lines, the stronger the magnetic field.

Here are a few illustrations. Note: the pictures are 2-dimensional, so they only show a 2D slice of the 3D space.

Field lines of a bar magnet

Another bar magnet

Field lines of a horseshoe magnet

Bar magnet versus solenoid

Breaking a magnet into 2 halves

Magnetic field of a current in a long straight wire

Right Hand Rule for the magnetic field of a current

Key Feature of Magnetic Field lines

• Magnetic field lines never cross each other.
  This is true for lines of any vector fields.
• Magnetic field lines never begin or end enywhere in space but either run to/from infinity or form closed loops.
• Unlike the electrostatic field lines, the magnetic field lines usually form closed loops.