Magnetic Field Lines

A magnetic field is pictured, exactly like an electric field, using continuous curves called magnetic field lines: the tangent to a line at any point gives the direction of $\vec{B}$ there, and the density of the lines (how closely packed they are) represents the magnitude of $\vec{B}$. Several of the rules are shared with electric field lines, but ONE crucial rule is different, with real physical meaning.

Shared properties. (1) Field lines never cross -- at any point, $\vec{B}$ has one, and only one, direction, so two lines crossing would mean two directions at once, which is impossible. (2) Line density shows field strength -- lines bunch closely near the poles, where $B$ is large, and spread apart farther away, where $B$ is smaller. (3) Outside the magnet, the lines emerge from the N pole and curve around to enter the S pole, exactly like the electric dipole's field lines running from $+q$ to $-q$.

The one crucial difference: field lines form CLOSED LOOPS. Unlike electric field lines, which always begin on a positive charge (or infinity) and end on a negative charge (or infinity) and are never continued inside the source charge itself, magnetic field lines CONTINUE right through the interior of the magnet, running from the S pole back to the N pole INSIDE the material (Figure 1). Every single magnetic field line is therefore a continuous, unbroken CLOSED LOOP, with no true beginning and no true end anywhere. This reflects a deep fact confirmed by every experiment ever performed: an isolated magnetic pole (a magnetic "monopole", the analogue of a single isolated electric charge) has never been observed to exist (Section 1.4), so a magnetic field line can never simply terminate the way an electric field line does at a charge -- it must always close on itself. …