Ranking three solenoids

Problem

Three cylindrical solenoids, all carrying the same current $I$: A ($n = 1000$ turns/m), B ($n = 500$ turns/m), C ($n = 2000$ turns/m). Rank the magnetic fields inside them from smallest to largest.

Solution

The field inside an ideal solenoid is

$B = \mu_0 n I$

For the same current $I$, the field is directly proportional to the turn density $n$: $B \propto n$. So the solenoid with more turns per metre has the largest field.

Ranking from smallest to largest: $B_B\,(500) < B_A\,(1000) < B_C\,(2000)$.

$\ev{B_C > B_A > B_B}$

Links

Topics: Magnetism Concepts: Magnetic field Skills: Ranking reasoning