The solenoid

A solenoid is a series of stacked loops, all carrying the same current. Its magnetic effect is that of a long cylindrical magnet: it concentrates an intense, uniform field inside itself, almost zero outside.

Law — Field of an ideal solenoid

Inside a solenoid of $N$ loops, length $L$, carrying current $i$, the field is uniform and parallel to the axis: $\ev{|\vec{B}|_\text{int} = \mu_0\,i\,\frac{N}{L}}$ Outside, $|\vec{B}|_\text{ext}\approx 0$.

The ratio $n = N/L$ appears, the number of turns per unit length: the field depends only on the winding density and the current, not on the diameter of the solenoid.

Ideal solenoid: uniform field parallel to the axis inside, practically zero outside.

Analogy

The solenoid is the magnetic analogue of the parallel-plate capacitor: it generates a uniform field inside itself (just as the capacitor generates a uniform $\vec{E}$) and an almost zero field outside.

The direction of $\vec{B}$: the hitchhiker’s rule. The formula gives the magnitude, not the direction. The direction depends on how the wire is wound and which way the current flows: reversing the current reverses $\vec{B}$. The most reliable way to determine it is the hitchhiker’s rule: curl the four fingers of the right hand around the solenoid, closed into a fist, in the same direction the current flows in the loops; the extended thumb, like that of a hitchhiker, indicates the direction of the field $\vec{B}$ inside.

Hitchhiker’s rule: right-hand fingers curled in the direction of the current, thumb along $\vec{B}$ inside the solenoid.

Always the right hand

The rule always holds with the right hand. Using the left hand gives the opposite direction and is certainly wrong. It can also be used in reverse: knowing the direction of $\vec{B}$ (for example with a compass), place the right thumb in that direction and the fingers show the direction the current flows.

Collegamenti

Argomenti: Magnetismo Concetti: Campo magnetico · Teorema di Ampère Competenze: Regola della mano destra

Esercizi collegati: Dimensional check of the solenoid field · Field inside a solenoid · Problem — B field in a charging capacitor