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Section summary

  • An emf induced by motion relative to a magnetic field B is called a motional emf and is given by
    emf = Bℓv ( B , , and v perpendicular), size 12{"emf"=Bℓv} {}
    where size 12{ℓ} {} is the length of the object moving at speed v size 12{v} {} relative to the field.

Conceptual questions

Why must part of the circuit be moving relative to other parts, to have usable motional emf? Consider, for example, that the rails in [link] are stationary relative to the magnetic field, while the rod moves.

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A powerful induction cannon can be made by placing a metal cylinder inside a solenoid coil. The cylinder is forcefully expelled when solenoid current is turned on rapidly. Use Faraday’s and Lenz’s laws to explain how this works. Why might the cylinder get live/hot when the cannon is fired?

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An induction stove heats a pot with a coil carrying an alternating current located beneath the pot (and without a hot surface). Can the stove surface be a conductor? Why won’t a coil carrying a direct current work?

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Explain how you could thaw out a frozen water pipe by wrapping a coil carrying an alternating current around it. Does it matter whether or not the pipe is a conductor? Explain.

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Problems&Exercises

Use Faraday’s law, Lenz’s law, and RHR-1 to show that the magnetic force on the current in the moving rod in [link] is in the opposite direction of its velocity.

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If a current flows in the Satellite Tether shown in [link] , use Faraday’s law, Lenz’s law, and RHR-1 to show that there is a magnetic force on the tether in the direction opposite to its velocity.

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(a) A jet airplane with a 75.0 m wingspan is flying at 280 m/s. What emf is induced between wing tips if the vertical component of the Earth’s field is 3 . 00 × 10 5 T size 12{3 "." "00" times "10" rSup { size 8{ - 5} } `T} {} ? (b) Is an emf of this magnitude likely to have any consequences? Explain.

(a) 0.630 V

(b) No, this is a very small emf.

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(a) A nonferrous screwdriver is being used in a 2.00 T magnetic field. What maximum emf can be induced along its 12.0 cm length when it moves at 6.00 m/s? (b) Is it likely that this emf will have any consequences or even be noticed?

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At what speed must the sliding rod in [link] move to produce an emf of 1.00 V in a 1.50 T field, given the rod’s length is 30.0 cm?

2.22 m/s

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The 12.0 cm long rod in [link] moves at 4.00 m/s. What is the strength of the magnetic field if a 95.0 V emf is induced?

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Prove that when B size 12{B} {} , size 12{ℓ} {} , and v size 12{v} {} are not mutually perpendicular, motional emf is given by emf = Bℓv sin θ size 12{"emf"=Bℓv"sin"θ} {} . If v size 12{v} {} is perpendicular to B size 12{B} {} , then θ size 12{θ} {} is the angle between size 12{ℓ} {} and B size 12{B} {} . If size 12{ℓ} {} is perpendicular to B size 12{B} {} , then θ size 12{θ} {} is the angle between v size 12{v} {} and B size 12{B} {} .

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In the August 1992 space shuttle flight, only 250 m of the conducting tether considered in [link] could be let out. A 40.0 V motional emf was generated in the Earth’s 5 . 00 × 10 5 T size 12{5 "." "00" times "10" rSup { size 8{ - 5} } `T} {} field, while moving at 7 . 80 × 10 3 m/s size 12{7 "." "80" times "10" rSup { size 8{3} } `"m/s"} {} . What was the angle between the shuttle’s velocity and the Earth’s field, assuming the conductor was perpendicular to the field?

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Integrated Concepts

Derive an expression for the current in a system like that in [link] , under the following conditions. The resistance between the rails is R , the rails and the moving rod are identical in cross section A and have the same resistivity ρ . The distance between the rails is l, and the rod moves at constant speed v perpendicular to the uniform field B . At time zero, the moving rod is next to the resistance R .

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Integrated Concepts

The Tethered Satellite in [link] has a mass of 525 kg and is at the end of a 20.0 km long, 2.50 mm diameter cable with the tensile strength of steel. (a) How much does the cable stretch if a 100 N force is exerted to pull the satellite in? (Assume the satellite and shuttle are at the same altitude above the Earth.) (b) What is the effective force constant of the cable? (c) How much energy is stored in it when stretched by the 100 N force?

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Integrated Concepts

The Tethered Satellite discussed in this module is producing 5.00 kV, and a current of 10.0 A flows. (a) What magnetic drag force does this produce if the system is moving at 7.80 km/s? (b) How much kinetic energy is removed from the system in 1.00 h, neglecting any change in altitude or velocity during that time? (c) What is the change in velocity if the mass of the system is 100,000 kg? (d) Discuss the long term consequences (say, a week-long mission) on the space shuttle’s orbit, noting what effect a decrease in velocity has and assessing the magnitude of the effect.

(a) 10.0 N

(b) 2.81 × 10 8 J

(c) 0.36 m/s

(d) For a week-long mission (168 hours), the change in velocity will be 60 m/s, or approximately 1%. In general, a decrease in velocity would cause the orbit to start spiraling inward because the velocity would no longer be sufficient to keep the circular orbit. The long-term consequences are that the shuttle would require a little more fuel to maintain the desired speed, otherwise the orbit would spiral slightly inward.

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Questions & Answers

what is nuclear reaction?
Velina Reply
In a chemical reaction, you have atoms being rearranged in different patterns, so you end up with the same atoms but different molecules. In a nuclear reaction, you go one step deeper: you rearrange protons and neutrons, do you end up with different atoms.
Adrian
So, for example, stars fuse 2 Hydrogen atoms into 1 Helium atom (that's called nuclear fusion). Nuclear reactors break down heavy unstable atoms into smaller ones (that's nuclear fission)
Adrian
whats drag force?
Muhsin Reply
who can explain me about the connecting between energy and work? I don't understand about the equation of the formula
The Reply
Energy can be defined as the ability an object has to do work. so lets say if u want to move something from one place to another you would need energy to do it. a table a certain distance, but if u dont have energy that means you will not be able to move it. Work=Force×distance.
Mario
from work-kinetic energy theorem we get that work=change in kinetic energy
Mario
what is thermo electric thermometer
Undie Reply
Who can help me with dynamics?
ivan Reply
can someone enumerate the First and second law of thermodynamics
oladele Reply
radiation of phones kept amazing me
Okugbesan Reply
f=m(v-u)/t
Adeleke Reply
why acceleration due to gravity varies from place to place
Adeleke
I understand light is a range of wavelenghts from em spectrum, but Where do photons come from in particular, how it is emitted from the sun?
Ian Reply
please what is the formula for calculating Newton second law of motion?
Ogodo Reply
F=ma
pierre
what is emotion
Lilian Reply
properties of transverse waves
Abiodun Reply
is visible light electromagnetic wave?
akash Reply
Visible light is a range of wavelengths within the electro magnetic spectrum.
Robert
It is electro magnetic radiation from the sun.
Robert
please what is the formula for coefficient of kinetic friction
Seyi Reply
What is work
Sunbomustaphar Reply

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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