Emf That Appears  Called a Self

Chapter 30 Induction and Inductance 30-7 Inductors and Inductance

Capacitor used  to produce a desired electric field. Inductor used  to produce a desired magnetic field. Inductance inductor 

Inductance of a Solenoid

long solenoid  of cross-sectional area A what is the inductance per unit length near its middle? The flux linkage  for this section of the solenoid 

120 Chapter 30 Induction and Inductance

30-8 Self-Induction

If two inductors  near each other  a current i in

one  produces a magnetic flux  through the second.

Changing i  produces a change in .

This process  (see Fig. 30-18) called self- induction,  emf that appears  called a self-

induced emf.

FIG.30-18  the current in

a coil is changed by varying

the contact position on a variable resistor  self-induced emf  appears in the

coil while the current is

changing.

121

Chapter 30 Induction and Inductance

In any inductor  coil  solenoid  toroid self-induced

emf appears whenever the current changes with time.

The magnitude  of the current has no influence on the magnitude of the induced emf  only the rate of change of the current counts.

The direction  of a self-induced emf  find from

Lenz's law

122 Chapter 30 Induction and Inductance

Ans: d and e 30-9 RL Circuits Section 27-9  if an emf introduce suddenly into a

single-loop circuit containing R  C  the charge on the

capacitor does not build up immediately to its final

equilibrium value C  but approaches it in an exponential fashion:

Analogous  if an emf introduce suddenly into a single-loop circuit containing R  L.

Self-induced emf  opposes the rise of the current

 the battery emf' in polarity.

123 Chapter 30 Induction and Inductance

124 Chapter 30 Induction and Inductance

FIG. 30-22  The variation

with time of  (a) VR  the potential difference across the resistor in the

circuit of Fig. 30-21,.

125 Chapter 30 Induction and Inductance

FIG. 30-22  The variation

with time of  (b) VL  the potential difference across

the inductor in that circuit.

Small triangles  represent successive

intervals of one inductive time constant L =

LlR.

In the figure  R = 2000  L = 4.0 H   = 10 V.

If S in Fig. 30-20  thrown to b  the battery

removed  from the circuit The differential equation  governs the decay can

be found by putting  = 0  in Eq. 30-39:

126 Chapter 30 Induction and Inductance

Both current  rise  decay  governed by the same

inductive time constant L

127