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Chapter 23: Q17PE (page 860)

(a) A jet airplane with a 75.0 mwingspan is flying at 280 m /s. What emf is induced between wingtips if the vertical component of the Earth鈥檚 field is3.00脳10-5T? (b) Is an emf of this magnitude likely to have any consequences? Explain.

Short Answer

Expert verified
  1. The emf induced is obtained as: 0.63 V.
  2. No, there are no consequences for such small emf.

Step by step solution

01

Given Data

Wingspan of jet is 75.0 m.

Velocity of jet is 280 m/s

Vertical component of Earth鈥檚 magnetic field is3.00脳10-5T

02

Define Electromagnetic Induction

The creation of an electromotive force across an electrical conductor in a changing magnetic field is known as electromagnetic or magnetic induction. Induction was discovered in by Michael Faraday, and it was mathematically characterized as Faraday's law of induction by James Clerk Maxwell.

03

Evaluating the emf included(a)

The motional emf will be simply given by the equation:

e=BLv鈥︹赌︹赌︹赌︹赌︹赌�..(1)

The value of B is the magnetic field, the value of L is the length of the wingspan, and the value of v is the velocity.

Substituting the given data in equation (1) will give,

蔚=3.00脳10-5T脳75m脳280m/s=0.63V

Therefore, the emf induced is: 0.63 V.

04

Explanation of part(b)

Such emf is not likely to create any problem in the functioning of the aircraft. Then also, friction with the air creates charges, and then it leads to the planes having sharp edges where they can discharge these charges from.

Therefore, emf of this magnitude does not have any consequences.

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Most popular questions from this chapter

The capacitor in Figure\(23.55\)(b) will filter high-frequency signals by shorting them to earth/ground. (a) What capacitance is needed to produce a reactance of\(10.0{\rm{ }}m\Omega \)for a\(5.00{\rm{ }}kHz\)signal? (b) What would its reactance be at\(3.00{\rm{ }}Hz\)? (c) Discuss the implications of your answers to (a) and (b).

(a) If the emf of a coil rotating in a magnetic field is zero at \(t = 0\) , and increases to its first peak at, \(t = 0.100ms\) what is the angular velocity of the coil?

(b) At what time will its next maximum occur?

(c) What is the period of the output?

(d) When is the output first one-fourth of its maximum?

(e) When is it next one-fourth of its maximum?

A multipurpose transformer has a secondary coil with several points at which a voltage can be extracted, giving outputs of 5.60, 12.0, and 480 V. (a) The input voltage is 240 V to a primary coil of 280 turns. What are the numbers of turns in the parts of the secondary used to produce the output voltages? (b) If the maximum input current is 5.00 A, what are the maximum output currents (each used alone)?

Your \(RL\) circuit has a characteristic time constant of \(20.0{\rm{ }}ns\), and a resistance of \(5.00{\rm{ }}M\Omega \). (a) What is the inductance of the circuit? (b) What resistance would give you a \(1.00{\rm{ }}ns\) time constant, perhaps needed for quick response in an oscilloscope?

The heating coils in a hair dryer are \(0.800{\rm{ }}cm\) in diameter, have a combined length of \(1.00{\rm{ }}m\), and a total of \(400\) turns. (a) What is their total self-inductance assuming they act like a single solenoid? (b) How much energy is stored in them when \(6.00{\rm{ }}A\) flows? (c) What average emf opposes shutting them off if this is done in \(5.00{\rm{ }}ms\) (one-fourth of a cycle for \(50{\rm{ }}Hz\) AC)?

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