30. Induction and Inductance

A single loop of wire with a current of 0.3A produces a flux of 0.005 Wb. If the self-induced EMF on this loop is 10 mV, how quickly must the current be changing?

A long, straight solenoid has 800 turns. When the current in the solenoid is 2.90 A, the average flux through each turn of the solenoid is 3.25 × 10^-3 Wb. What must be the magnitude of the rate of change of the current in order for the self-induced emf to equal 6.20 mV?

At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. If the inductor is a solenoid with 400 turns, what is the average magnetic flux through each turn when the current is 0.720 A?

At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. What is the inductance of the inductor?

A 2.50-mH toroidal solenoid has an average radius of 6.00 cm and a cross-sectional area of 2.00 cm². How many coils does it have? (Make the same assumption as in Example 30.3.)

Inductance of a Solenoid. A metallic laboratory spring is typically 5.00 cm long and 0.150 cm in diameter and has 50 coils. If you connect such a spring in an electric circuit, how much self-inductance must you include for it if you model it as an ideal solenoid?

A pair of straight parallel thin wires, such as a lamp cord, each of radius r, are a distance 𝓁 apart and carry current to a circuit some distance away. Ignoring the field within each wire, show that the inductance per unit length is (μ₀/π) ln[(𝓁 - r) /r].

Determine the inductance L of a 0.60-m-long air-filled solenoid 2.9 cm in diameter containing 7500 loops.

(I) What is the inductance of a coil if the coil produces an emf of 2.20 V when the current in it changes from -28.0 mA to +25.0 mA in 12.0 ms?

A coil has 3.25-Ω resistance and 440-mH inductance. If the current is 3.00 A and is increasing at a rate of 3.15 A/s, what is the potential difference across the coil at this moment?

The wire of a tightly wound solenoid is unwound and used to make another tightly wound solenoid of 2.2 times the diameter. By what factor does the inductance change?

(III) A toroid has a rectangular cross section as shown in Fig. 30–26. Show that the self-inductance is

$L=\frac{{\mu }_0{N}^{2}h}{2\pi }\ln \frac{r_2}{r_1}$

where N is the total number of turns and r₁, r₂ and h are the dimensions shown in Fig. 30–26. [Hint: Use Ampère’s law to get B as a function of r inside the toroid, and integrate.]

An air-filled toroidal solenoid has a mean radius of 15.0 cm and a cross-sectional area of 5.00 cm². When the current is 12.0 A, the energy stored is 0.390 J. How many turns does the winding have?

An amateur radio operator wishes to build a receiver that can tune a range from 14.0 MHz to 15.0 MHz. A variable capacitor has a minimum capacitance of 95 pF.

(a) What is the required value of the inductance?

(b) What is the maximum capacitance used on the variable capacitor?