Wind more turns into a shorter coil, push more current through it, then drop in an iron core and watch the field — and the pull on the pole face — jump by orders of magnitude.
Field in the core B = μrμ0nI
5.03 mT
101 × Earth's field
CORE SATURATED
Holding force F = B²A / 2μ0
0.00101 N
holds about 0.1 g
Turns, N500
Coil length, L0.250 m
Current, I2.0 A
Core2000 turns/m
Pole face A = 1.0 cm² · air μr = 1, soft iron μr = 200 · iron saturates at 2.0 T
Tip: turns and length only ever act as the ratio n = N/L. Doubling N and doubling L leaves the field exactly where it was.