Given i 10 a n 500 turns g 5 mm a 20 mm and b 2 mm

Question

Let the coil of the solenoid of Problem 12.4.6 have a resistance R and be excited by a voltage v = V_m sin ωt. Consider a plunger displacement of g = g₀.

(a) Obtain the expression for the steady-state coil current.

(b) Obtain the expression for the steady-state electric force.

Problem 12.4.6

Consider the solenoid with a core of square cross section shown in Figure P12.4.6.

(a) For a coil current I (dc), derive an expression for the force on the plunger.

(b) Given I = 10 A, N = 500 turns, g = 5 mm, a = 20 mm, and b = 2 mm, calculate the magnitude of the force.