where C is a proportionality constant, A is the cross-sectional area of the plunger, N is the number of turns in the solenoid, I is the current through the solenoid wire, and ℓ is the length of the solenoid. For units using inches, pounds force, and amperes with long, slender, solenoids, the value of C is around 0.009 to 0.010 psi (maximum pull pounds per square inch of plunger cross-sectional area). For example, a 12-inch long coil (ℓ = 12 in) with a long plunger of 1-square inch cross section (A = 1 in) and 11,200 ampere-turns (N I = 11,200 Aturn) had a maximum pull of 8.75 pounds (corresponding to C = 0.0094 psi).