6-8. One method of measuring magnetization is to place the sample in a field gra

Question

6-8. One method of measuring magnetization is to place the sample in a field gradient dHldr, and measure the resulting force in the x-direction. (a) From the magnetic energy per unit volume (EoH12-see Problem 5-13), calculate the force per unit volume in an applied field of 1000 A/cm and a field gradient of 1000 A/cm2 on (a) a Type I superconductor (assume that the critical field is not exceeded), (b) a soft ferromagnet with a relative perme- ability of 10, and (c) a paramagnet with a susceptibility of 104. For each of these materials-superconductor, ferromagnet, paramagnet-is the force ex- erted in the direction of increasing or decreasing field?

Explanation / Answer

6-8 .

Given

a. E = -uo*XmH^2/2

hence froce per unit volume = -dE/dx

F = -dE/dx = uo*Xm*H*(dH/dx)

dH/dx = 1000 A/cm^2

H = 1000 A/cm

uo = 4*pi*10^-7

a. type I superconductor

Xm = -1

relative permeability = 0 = k

hence

F = k*uo*Xm*HdH/dx

k = 0

hence F = 0

very small force in the direction of decreasing field is observed

b. k = 10^6

Xm = 1

hence

F = 1256637061435.9172953 N

very large force in the direction of the increasing field is observed

c. paramagnet

Xm = 10^-4

k = 1 ( slightly greater than 1)

hence

F = 125.663706143591729 N

force in the fdirection of increasing field is observed

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