# Magnetic Circuit and Plunger

1. Jul 25, 2010

### dhruv.tara

1. The problem statement, all variables and given/known data
The magnetic circuit consists of a core, a movable plunger of length lp, permeability mu, area Ac and mean length lC. the overlap area is the function of x,
Ag = Ac(1- (x/xO))
Neglect fringing.
(Also in the figure for simpler calculations I have assumed lp= g)

a) For the mu--> infinite, derive an expression for the magnetic flux density in air gap as the function of coil current and area of gap as x is varied from 0<=x<=0.8xO. Also what is the corresponding flux density in the core?

I do not have solutions to either of the problems, please tell me if I am on right track or not?

b) Repeat the problem for a finite mu.

2. Relevant equations

3. The attempt at a solution

For the part (a) of the solution, I tried to solve as follows:
Bg = phiG/areaG = phi/areaG (no fringing)
I solved for phi = NI/ReluctanceTotal
Got phi = NI*muO*Ac*(xO-x)/(lp*xO)
Bg = phi/Ag cancelled the terms that varied with x and I got the constant result as
Bg = NI*muO/lp

I also see this solution as I think that here we are calculating the magnetic flux density. And as the plunger is also of the infinite permeability there should be no effect on flux per unit area (flux density)

But I wonder if the plunger would have been of an irregular shape, say an oval then should I get a change in magnetic flux density?

For part (b) of the solution, I see the plunger and core to be in a series resistance. So I break the core resistance into 2 parts as main core resistance (Sc1) and as plunger resistance (Sc2) and one as air gap resistance.

Sc1 = lCore/(mu*aCore)
Sc2 = lp*xO/(mu*x*aCore)
Sgap = lp*xO/(muO*aCore*(xO-x))

I get the total reluctance and then put it into B and get somewhat complicated expression that does depend upon x. Would this be true?

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Last edited: Jul 25, 2010