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The solenoid and toroid are the two most important Ampere's law applications. An ideal solenoid (infinite, tightly wound) has uniform field $B = \mu_0 nI$ inside ($n$ = turns per unit length) and zero field outside. At the end of a finite solenoid: $B = \mu_0 nI/2$. The field is parallel to the axis, and the solenoid externally resembles a bar magnet.

A toroid is a solenoid bent into a ring with $N$ total turns: $B = \mu_0 NI/(2\pi r)$ inside the toroid. Unlike the solenoid, the field varies across the cross-section ($B \propto 1/r$). For thin toroids, this variation is negligible. Critically, $B = 0$ both outside the toroid AND inside the central hole — no current is enclosed in either region.

Common JEE traps: (1) Using total turns $N$ instead of turns per unit length $n = N/L$ in the solenoid formula. (2) Assuming the toroid's central hole has a field (it doesn't). (3) Confusing $B$ inside the toroid windings with $B$ in the hole. (4) Applying the solenoid formula to a toroid or vice versa. Coaxial solenoids follow superposition: fields add or subtract based on current directions.