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

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours .(Ah)A50AhA battery can supply a current of50Afor 1.0h,or25Afor2.0hor for and so on. (a) What total energy can be supplied by a 12-v,60-Ahbattery if its internal resistance is negligible? (b) What volume (in litres) of gasoline has a total heat of combustion equal to the energy obtained in part (a)? (See Section 17.6; the density of gasoline is 900kg/m3.) (c) If a generator with an average electrical power output ofrole="math" localid="1655719210000" 0.45kW is connected to the battery, how much time will be required for it to charge the battery fully?

In the circuit shown in Fig. E26.18,ε=36.V,R1=4.0Ω,R2=6.0Ω,R3=3.0Ω(a) What is the potential difference Vab between points a and b when the switch S is open and when S is closed? (b) For each resistor, calculate the current through the resistor with S open and with S closed. For each resistor, does the current increase or decrease when S is closed?

Two coils are wound around the same cylindrical form. When the current in the first coil is decreasing at a rate of , the induced emf in the second coil has magnitude 1.65×10-3V. (a) What is the mutual inductance of the pair of coils? (b) If the second coil has 25 turns, what is the flux through each turn when the current in the first coil equals 1.20A? (c) If the current in the second coil increases at a rate of 0.360A/s, what is the magnitude of the induced emf in the first coil?

A fuse is a device designed to break a circuit, usually by melting when the current exceeds a certain value. What characteristics should the material of the fuse have?

(a) At room temperature, what is the strength of the electric field in a

12-gauge copper wire (diameter 2.05mm) that is needed to cause a 4.50-A

current to flow? (b) What field would be needed if the wire were made of silver

instead?

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