30. Induction and Inductance

A voltage $v\left(t\right)=10cos\left(2000\omega t\right)$ is applied to a $100-\mathrm{mH}$ inductor. What is the expression for the current $i\left(t\right)$ through the inductor (assume zero initial current)?

Which of the following expressions gives the energy stored in an ideal inductor with inductance $L$ carrying a current $I$?

In an $RL$ circuit with a resistor and an inductor in series connected to a constant voltage source, what effect does increasing the inductance of the inductor have on the rate at which the current reaches its maximum steady-state value after the circuit is closed?

The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. The potential between points a and b is V_ab = 1.04 V, with point a at higher potential. Is the current increasing or decreasing?

(II) For the toroid of Fig. 30–26, determine the energy density in the magnetic field as a function of r(r₁ < r < r₂) and integrate this over the volume to obtain the total energy stored in the toroid, which carries a current I in each of its N loops.

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It is proposed to store 1.00 kWh = 3.60 × 10⁶ J of electrical energy in a uniform magnetic field with magnitude 0.600 T. If instead this amount of energy is to be stored in a volume (in vacuum) equivalent to a cube 40.0 cm on a side, what magnetic field is required?

Which of the following expressions correctly gives the inductance of a closely packed solenoidal coil of length $l$, cross-sectional area $A$, number of turns $N$, and permeability $\mu$ of the core material?

A 30mH inductor carries a current of 500mA. If the circuit is opened and the current stops over a period of 3.0μs, what potential develops across the inductor?

It has been proposed to use large inductors as energy storage devices. How much electrical energy is converted to light and thermal energy by a 150 W light bulb in one day?

BIO MRI (magnetic resonance imaging) is a medical technique that produces detailed 'pictures' of the interior of the body. The patient is placed into a solenoid that is 40 cm in diameter and 1.0 m long. A 100 A current creates a 5.0 T magnetic field inside the solenoid. To carry such a large current, the solenoid wires are cooled with liquid helium until they become superconducting (no electric resistance). How much magnetic energy is stored in the solenoid? Assume that the magnetic field is uniform within the solenoid and quickly drops to zero outside the solenoid.

CALC FIGURE P30.67 shows the potential difference across a 20 mH inductor. The current through the inductor at t = 0 ms is 0.25 A. What is the current at t = 10 ms?

What is the energy density at the center of a circular loop of wire carrying a 19.0-A current if the radius of the loop is 28.0 cm?

When the current in a toroidal solenoid is changing at a rate of 0.0260 A/s, the magnitude of the induced emf is 12.6 mV. When the current equals 1.40 A, the average flux through each turn of the solenoid is 0.00285 Wb. How many turns does the solenoid have?

A long straight wire of radius r carries current I uniformly distributed across its cross-sectional area. Find the magnetic energy stored per unit length in the interior of this wire.

Assuming the Earth’s magnetic field averages about 0.50 x 10^-4 T near the surface of the Earth, estimate the total energy stored in this field in the first 5.0 km above the Earth’s surface.