14.2 Self-Inductance and Inductors

Current flows through the inductor in the figure from B to A instead of from A to B as shown. Is the current increasing or decreasing in order to produce the emf given in diagram (a)? In diagram (b)?

A changing current induces an emf of 10 V across a 0.25-H inductor. What is the rate at which the current is changing?

(a) Calculate the self-inductance of a solenoid that is tightly wound with wire of diameter 0.10 cm, has a cross-sectional area of $\left(0.90 \text{cm}\right)^{2}$, and is 40 cm long. (b) If the current through the solenoid decreases uniformly from 10 to 0 A in 0.10 s, what is the emf induced between the ends of the solenoid?

(a) What is the magnetic flux through one turn of a solenoid of self-inductance $8.0 \times 10^{−5} \text{H}$ when a current of 3.0 A flows through it? Assume that the solenoid has 1000 turns and is wound from wire of diameter 1.0 mm. (b) What is the cross-sectional area of the solenoid?

Does self-inductance depend on the value of the magnetic flux? Does it depend on the current through the wire? Correlate your answers with the equation $N \Phi_{\text{m}} = L I .$

Discuss how you might determine the self-inductance per unit length of a long, straight wire.

How does the self-inductance per unit length near the center of a solenoid (away from the ends) compare with its value near the end of the solenoid?

An emf of 0.40 V is induced across a coil when the current through it changes uniformly from 0.10 to 0.60 A in 0.30 s. What is the self-inductance of the coil?

What is the rate at which the current though a 0.30-H coil is changing if an emf of 0.12 V is induced across the coil?

A coil with a self-inductance of 2.0 H carries a current that varies with time according to $I \left(t\right) = \left(2.0 \text{A}\right) \text{sin} 120 \pi t .$ Find an expression for the emf induced in the coil.

A coil with a self-inductance of 3.0 H carries a current that decreases at a uniform rate $d I / d t = −0.050 \text{A}/\text{s}$. What is the emf induced in the coil? Describe the polarity of the induced emf.

A long, cylindrical solenoid with 100 turns per centimeter has a radius of 1.5 cm. (a) Neglecting end effects, what is the self-inductance per unit length of the solenoid? (b) If the current through the solenoid changes at the rate 5.0 A/s, what is the emf induced per unit length?

What is the self-inductance per meter of a coaxial cable whose inner radius is 0.50 mm and whose outer radius is 4.00 mm?