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-in- duced 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 .