Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Motional emfs in Transportation. Airplanes and trains move through the earth’s magnetic field at rather high speeds, so it is reasonable to wonder whether this field can have a substantial effect on them. We shall use a typical value of 0.50 G for the earth’s field.

(a) The French TGV train and the Japanese “bullet train” reach speeds of up to 180 mph moving on tracks about 1.5 m apart. At top speed moving perpendicular to the earth’s magnetic field, what potential difference is induced across the tracks as the wheels roll? Does this seem large enough to produce noticeable effects?

(b) The Boeing 747-400 aircraft has a wingspan of 64.4 m and a cruising speed of 565 mph. If there is no wind blowing (so that this is also their speed relative to the ground), what is the maximum potential difference that could be induced between the opposite tips of the wings? Does this seem large enough to cause problems with the plane?

Short Answer

Expert verified
  1. Potential difference is induced across the tracks as the wheels roll is 0.6 mV and this is very small to be noticeable.
  2. The maximum potential difference that could be induced between the opposite tips of the wings is 0.813V and this is also very small to be noticeable thus it does not cause problems with the plane.

Step by step solution

01

Concept

A conductor moving in a magnetic field may have a potential difference induced across it, depending on how it is moving. The magnitude of that induced emf is,

ε=vBLsin(ϕ)

02

Calculation

  1. We have a train with a speed of 180 mph moving on tracks about 1.5 m apart, it is moving perpendicularly to the earth's field (B = 0.50 G), so = 90.0°, substitute with the givens we get (note that l m/s = 2237 mph and 1 G =10 T), so we get

ε=vBLsin(ϕ)

03

Calculation

(a) We have a train with a speed of 180 mph moving on tracks about 1.5 m apart, it is moving perpendicularly to the earth's field (B = 0.50 G), so = 90.0°, substitute with the givens we get (note that l m/s = 2237 mph and 1 G =10 T), so we get

ε=(180mph)1m/s2.237mph0.50×10-4T1.5mε=6.0×10-3V=6.0mV

(b) For a Boeing aircraft, which has a wingspan of 644 m and a cruising speed of 565 mph, the induced emf is, ε=565mph1m/s2.237mph(0.50×10-4T)(64.4m)ε=0.813V

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Section 27.2 describes a procedure for finding the direction of the magnetic force using your right hand. If you use the same procedure, but with your left hand, will you get the correct direction for the force? Explain.

A silver wire 2.6 mm in diameter transfers a charge of 420 C in 80

min. Silver containsfree electrons per cubic meter. (a) What is the

current in the wire? (b) What is the magnitude of thedrift velocity of the

electrons in the wire?

A particle with mass1.81×10-3kgand a charge of has1.22×10-8C, at a given instant, a velocityV=(3.00×104m/s).What are the magnitude and direction of the particle’s acceleration produced by a uniform magnetic fieldB=(1.63T)i+(0.980T)j^?

You connect a battery, resistor, and capacitor as in Fig. 26.20a, where R = 12.0 Ω and C = 5.00 x 10-6 F. The switch S is closed at t = 0. When the current in the circuit has a magnitude of 3.00 A, the charge on the capacitor is 40.0 x 10-6 C. (a) What is the emf of the battery? (b) At what time t after the switch is closed is the charge on the capacitor equal to 40.0 x 10-6 C? (c) When the current has magnitude 3.00 A, at what rate is energy being (i) stored in the capacitor, (ii) supplied by the battery

Question: A positive point charge is placed near a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a negative point charge of equal magnitude in the mirror image position behind the initial position of the plane. Is this correct? Why or why not?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free