0195136047.pdf

PROBLEMS 547

N turns

i

Cylindrical plunger

Spring

Nonmagnetic

cylindrical sleeve

t

x t

0

x 0 : position of plunger when spring is relaxed

x

Figure P12.4.1

12.4.2In Problem 12.4.1 neglect the saturation of the
core, leakage, and fringing. Neglect also the re-
luctance of the ferromagnetic circuit. Assuming
that the cross-sectional area of the center leg
is twice the area of the outer legs, obtain ex-
pressions for the inductance of the coil and the
electromagnetic force on the plunger.
*12.4.3For the electromagnet shown in Figure P12.4.3,
theλ–irelationship for the normal working range
is given byi=aλ^2 +bλ(x−d)^2 ,whereaandb
are constants. Determine the force applied to the
plunger by the electric system.
12.4.4A solenoid of cylindrical geometry is shown in
Figure P12.4.4.
(a) If the exciting coil carries a steady direct
currentI, derive an expression for the force
on the plunger.
(b) For the numerical valuesI=10 A,N= 500
turns,g=5 mm,a=20 mm,b=2 mm,

andl=40 mm, find the magnitude of the

force. Assume infinite permeability of the

core and neglect leakage.

12.4.5Let the solenoid of Problem 12.4.4 carry an al-

ternating current of 10 A (rms) at 60 Hz instead

of the direct current.

(a) Find an expression for the instantaneous

force.

(b) For the numerical values ofN, g, a, b,and

lgiven in Problem 12.4.4(b) compute the

average force. Compare it to that of Problem

12.4.4(b).

12.4.6Consider the solenoid with a core of square cross

section shown in Figure P12.4.6.

(a) For a coil currentI(dc), derive an expression

for the force on the plunger.

(b) GivenI=10 A,N=500 turns,g=5 mm,

a=20 mm, andb=2 mm, calculate the

magnitude of the force.

Plunger

Coil Coil

Cylindrical magnetic shell

d

x

++

++

++

Figure P12.4.3