phy1020.DVI

whereKmis called therelative permeabilityof the material. The combination

DKm 0 (37.13)

is called thepermeabilityof the material. Since the relative permeabiltiyKmis typically a number very close
to 1, it is convenient to introduce themagnetic susceptibilitym, defined by

KmD 1 Cm: (37.14)

37.4 Energy Stored in an Inductor.

An inductor can be thought of as a device that stores energy in the magnetic field between inside the coils of
the inductor. Using the calculus, it can be shown that the potential energyUstored in the magnetic field of
an inductor of inductanceLcarrying currentI, is given by

UD^12 LI^2 : (37.15)

Theenergy density(energy per unit volume) of an inductor can be found by using the solenoid as an example.
From Eq. (37.7), the total potential energy stored in a solenoid (of plate areaAand separationd)is

UD^12 LI^2 (37.16)

D^12  0 n^2 A`I^2 (37.17)

Since the magnetic field inside the solenoid isBD 0 nI, this gives

UD

1

2

. 0 nI/^2 .A`/

1

 0

(37.18)

D

1

2

1

 0

B^2 A` (37.19)

Since the volume inside the solenoid isA, the energy densityuDU=.A/,or

uD

1

2 0

B^2 : (37.20)

Compare this result with the analogous equation for a capacitor, Eq. (25.16):

uD^12 " 0 E^2 : (37.21)