30. Induction and Inductance

A thin rod moves in a perpendicular, unknown magnetic field. If the length of the rod is 10 cm and the induced EMF is 1 V when it moves at 5 m/s, what is the magnitude of the magnetic field?

(II) A 22.0-cm-diameter coil consists of 36 turns of circular copper wire 2.6 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 8.65 x 10⁻³ T/s. Determine (a) the current in the loop, and (b) the rate at which thermal energy is produced.

(II) A long horizontal wire carries 24.0 A of dc current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points downward, 38° below the horizontal, and has magnitude 5.0 x 10⁻⁵ T?

(I) A simple generator is designed to generate a peak output voltage of 24.0 V. The square armature consists of windings that are 5.15 cm on a side and rotates in a field of 0.380 T at a rate of 60.0 rev/s. How many loops of wire should be wound on the square armature?

(II) If 75 MW of power at 45 kV (rms) arrives at a town from a generator via transmission lines of total resistance 3.0 Ω, calculate (a) the emf at the generator end of the lines, and (b) the fraction of the power generated that is wasted in the lines.

(I) The moving rod in Fig. 29–12b is 12.0 cm long and is pulled at a speed of 15.0 cm/s. If the magnetic field is 0.650 T, calculate the emf developed.

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(III) A simple generator has a square armature 6.0 cm on a side. The armature has 85 turns of 0.65-mm-diameter copper wire and rotates in a 0.65-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0 W. At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

Two parallel resistanceless rails are 32 cm apart on a 6.0° ramp. They are joined at the bottom by a 0.60-Ω resistor. At the top a copper bar of mass 0.040 kg (ignore its resistance) is laid across the rails. Assuming a vertical 0.65-T magnetic field, what is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?