Chapter 37
Inductance
The space surrounding an electric circuit contains a magnetic field due to the electric currents running in the
circuit. By the Biot-Savart law, the magnetic fluxˆBis proportional to the currentI:
ˆBDLI: (37.1)Here the proportionality constantLis called theinductance. Of course, the magnetic flux at a given point in
space depends on a number of factors besides the current: it also depends on the distance from the current,
the permeability of free space, etc. The inductanceLcan be thought of as all these other factors lumped
together.
The SI unit of inductance is thehenry(H), named for the American physicist Joseph Henry. Since
magnetic flux is measured in webers and current in amperes, Eq. (37.1) indicates that one henry is equal to
one weber per ampere: 1 HD1 Wb/A.
37.1 Solenoid Inductor
One very common device for introducing inductance into an electric circuit is thesolenoid, which is a coil of
wire wrapped on an insulating cylinder. As discussed earlier in Section 31.9, the magnetic fieldBinside a
solenoid carrying a currentIis given by
BD 0 nI; (37.2)wherenDN=is the total number of turns of wireNdivided by the lengthof the solenoid. We can
find an expression for the inductanceLof a solenoid by starting with this equation forB. LetAbe the
cross-sectional area of the solenoid, and letNbe the total number of turns of wire. Then the magnetic field
passes throughNturns, each of which has areaA. The total area through which the magnetic field passes is
thereforeNA, and so the magnetic flux is
ˆBDB.NA/ (37.3)
D 0 NnIA (37.4)
D 0 n^2 IA`: (37.5)The inductanceLis then found to be