Textbook Guide Physics: Magnetic Quantum Number, Local Field, Paramagnetism

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PHY131H1 Full Course Notes

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Chapter 32 maxwell"s equations; magnetism of matter. 32-1 gauss" law for magnetic fields: the simplest magnetic structure that can exist is a magnetic dipole. Magnetic monopoles are assumed to not exist: gauss" law for magnetic fields states that the net magnetic flux through any gaussian surface, assuming it is closed, is zero the implication is that magnetic monopoles do not exist. , can be combined with maxwell"s law as: 32-5 magnetism and electrons: electrons have intrinsic angular momentum called spin angular momentum (or spin) represented by the vector value. , with which an intrinsic spin magnetic dipole moment is expressed as itself cannot be measured while its component along any axis can. can only have two quantized (restricted) values which differ only in sign. In the same manner, (bohr magneton: the energy associated with the orientation of the spin magnetic dipole moment in an external magnetic field (

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Faraday's law describes how electric fields and electromotive forces are generated from changing magnetic fields. This problem is a prototypical example in which an increasing magnetic flux generates a finite line integral of the electric field around a closed loop that surrounds the changing magnetic flux through a surface bounded by that loop. A cylindrical iron rod with cross-sectional area is oriented with its symmetry axis coincident with the z axis of a cylindrical coordinate system as shown. It has a uniform magnetic field inside that varies according to .

1. Find , the electromotive force (EMF) around a loop that is at distance R from the z axis, where R is restricted to the region outside the iron rod as shown. Take the direction shown in the figure as positive

2. Due to the cylindrical symmetry of this problem, the induced electric field can depend only on the distance R from the z axis, where R is restricted to the region outside the iron rod. Find this field

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Learning Goal: To work through astraightforward application of Faraday's law to find the EMF andthe electric field surrounding a region of increasing flux

Faraday's law describes how electric fields and electromotiveforces are generated from changing magnetic fields. This problem isa prototypical example in which an increasing magnetic fluxgenerates a finite line integral of the electric field around aclosed loop that surrounds the changing magnetic flux through asurface bounded by that loop. A cylindrical iron rod withcross-sectional area is oriented with its symmetry axis coincidentwith the z axis of a cylindrical coordinate system as shown. It hasa uniform magnetic field inside that varies according to . In otherwords, the magentic field is always in the positive z direction,and it has no other components.

For your convenience, we restate Faraday's law here: , where is theline integral of the electric field, and the magnetic flux is givenby , where is the angle between the magnetic field and the localnormal to the surface bounded by the closed loop.
Direction: The line integral and surface integral reverse theirsigns if the reference direction of or is reversed. The right-handrule applies here: If the thumb of your right hand is taken along ,then the fingers point along . You are free to take the loopanywhere you choose, although usually it makes sense to choose itto lie along the path of the circuit you are considering.

Find , the electromotive force (EMF) around a loop that is atdistance from the z axis, where is restricted to the region outsidethe iron rod as shown. Take the direction shown in the figure aspositive.
Express in terms of , , , , and any needed constants such as , ,and .
Due to the cylindrical symmetry of this problem, the inducedelectric field can depend only on the distance from the z axis,where is restricted to the region outside the iron rod. Find thisfield.
Express in terms of quantities given in the introduction (andconstants), using the unit vectors in the cylindrical coordinatesystem,r^ ,theta^ , and z^ .

1a) Faraday discovered that a current is induced in a coil

A) only when the N pole of a magnet is inside the coil
B) only when the S pole of a magnet is inside the coil
C) only when there is a magnetic field inside the coil
D) only when the magnetic field inside the coil is changing

1b). A conductor moves through a uniform magnetic field at speed v and has a motional emf V created across it. If the conductor were to move twice as fast through the magnetic field, the motional emf would be:

A) V
B) 2V
C) 4V
D) V/2
E) V/4

1c) In the conducting rail discussed in section 25.2 (where the rail is moving at constant speed), what can you say about the power input due to the person pulling on the rail and the power dissipated in the resistance?

A) Power input from pull = power dissipated in R
B) Power input from pull > power dissipated in R
C) Power input from pull < power dissipated in R

1d) The electric generator as shown in the reading generates electricity by:

A) rotating a loop inside a magnetic field
B) moving a magnet in and out of a loop
C) sliding a loop over a magnet
D) running current through a loop in a magnetic field

1e) The magnetic flux through a loop:

A) is proportional to the number of magnetic field lines going through it
B) depends just on the B field going through the loop
C) is maximized when the B field lines in the plane of the loop
D) is zero when the B field is perpendicular to the plane of the loop
E) doesn't depend on the direction of the B field

1f) According to Lenz's Law, the induced B field (due to the induced current) will:

A) be in the opposite direction of the existing B field
B) be in the same direction as the existing B field
C) be in the same direction as the change in the existing B field
D) be in the opposite direction of the change in the existing B field

1g) A stationary coil experiences a doubling of its magnetic field (no change in direction of the field) in a time T and has a given induced EMF. If the same change were to have happened in half the time (T/2), the induced EMF would have been:

A) half as large
B) the same
C) twice as large
D) one-fourth as large
E) four times as large

1h) Eddy currents:

A) make it hard to pull a nonmagnetic material through a magnetic field
B) make it hard to pull a magnetic material through a magnetic field
C) speed up a magnetic material moving through a magnetic field
D) speed up a nonmagnetic material moving through a magnetic field

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Textbook Guide Physics: Magnetic Quantum Number, Local Field, Paramagnetism

PHY131H1 Full Course Notes

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