Magnetic Lines of Force and Magnetic Field

Just as electrostatics uses electric lines of force to visualise the electric field due to charges, magnetism uses magnetic lines of force to visualise the magnetic field due to a magnet. By convention, magnetic lines of force originate at the north pole of a bar magnet and end at its south pole (in the region external to the magnet itself).

Magnetic lines of force obey four defining properties. (i) The lines of force of a magnet, or of a current-carrying solenoid, always form CLOSED loops. This is a genuinely different behaviour from an electric dipole, whose lines of force originate on the positive charge and terminate on the negative charge WITHOUT ever forming a complete loop. (ii) At any point, the direction of the net magnetic field $\vec B$ is given by the tangent to the magnetic line of force at that point, taken in the sense the line is drawn. (iii) The number of lines of force crossing a unit area (i.e. their density) decides the magnitude of the magnetic field $B$ there -- a tightly bunched set of lines means a strong field, a sparse set means a weak one. (iv) Magnetic lines of force never intersect one another; if two lines did cross, the field direction at that crossing point would not be unique, which is impossible.

The total number of lines of force threading a given surface is called the magnetic flux, denoted $\phi$, whose SI unit is the weber (Wb). For the special case of a uniform magnetic field directed normal (perpendicular) to a finite area $A$, the magnitude of the field at a point in that area is $B=\dfrac{\phi}{A}$ (Eq. 12.1). Consequently, the SI unit of the magnetic field $B$ itself is weber per square metre, more commonly called the tesla (T), with the practical conversion $1\text{ Tesla}=10^4\text{ Gauss}$. …