Figure shows a circularly symmetric system in which a moveable plunger (constrained to move only in the vertical direction) is supported by a spring of spring constant K 5 28 N m The system is excited by a samarium cobalt permanent magnet in the shape of a washer of outer radius R 3 , inner radius R 2 , and thickness tm The system dimensions are R 1 2 1 cm, R 2 4 cm, R 3 4 5 cm, h 1 cm, g 1 mm, t m 3 mm The equilibrium position of the plunger is observed to be x 1 0 mm a Find the magnetic flux density B g in the fixed gap and B x in the variable gap b Calculate the x directed magnetic force pulling down on the plunger c The spring force is of the form f spring K (X 0 x) Find X 0 Spring Plunger g R R2 Magnet Im R3 C L

Question: Figure shows a circularly symmetric system in which a moveable plunger (constrained to move only in the vertical direction) is supported by a spring of

Figure shows a circularly symmetric system in which a moveable plunger (constrained to move only in the vertical direction) is supported by a spring of spring constant K = 5.28 N/m. The system is excited by a samarium-cobalt permanent-magnet in the shape of a washer of outer radius R₃, inner radius R₂, and thickness tm. The system dimensions are:

R₁ = 2.1 cm, R₂ = 4 cm, R₃ = 4.5 cm, h = 1 cm, g = 1 mm, t_m = 3 mm. The equilibrium position of the plunger is observed to be x = 1.0 mm.

a. Find the magnetic flux density B_g in the fixed gap and B_x in the variable gap.

b. Calculate the x-directed magnetic force pulling down on the plunger.

c. The spring force is of the form f _spring = K (X₀ ? x). Find X₀.

Spring Plunger g R R2 Magnet Im R3 C/L

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