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ORANGE COUNTRY
GO COWBOYS
PHYS 2114
LECTURE 14
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
Problem A cosmic-ray proton in interstellar space has energy of 10.0MeV and executes a circular orbit
having a radius equal to that of Mercury’s orbit around the Sun (5.80x1010m). Calculate the magnetic
field in that region of space.
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ORANGE COUNTRY
GO COWBOYS
PHYS 2114
ORANGE COUNTRY
GO COWBOYS
LECTURE 14
Instructor: Professor Donna Bandy
Magnetic Flux:
Problem In the figure below is an edge view of a 10-cm-diameter circular loop rotating in a uniform
0.050T magnetic field. Calculate the magnetic flux through the loop when is 0o, 30o, 60o, and 90o.
B-field

A
edge view
A
Circular Loop
Absence of magnetic monopoles: One of Maxwell’s Equations: The net magnetic flux
through any closed surface is always zero.
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ORANGE COUNTRY
GO COWBOYS
PHYS 2114
ORANGE COUNTRY
GO COWBOYS
LECTURE 14
Instructor: Professor Donna Bandy
Magnetic Dipoles, Monopoles, and Torque on a Magnetic Dipole
Magnetic dipole moment
Electric dipole
Torque on a on a current loop
Torque on Electric Dipole
Energy of a magnetic dipole
Energy of a electric dipole
3
ORANGE COUNTRY
GO COWBOYS
PHYS 2114
LECTURE 14
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
4
ORANGE COUNTRY
GO COWBOYS
PHYS 2114
LECTURE 14
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
Torque on a current loop in a uniform magnetic field
5
ORANGE COUNTRY
GO COWBOYS
PHYS 2114
LECTURE 14
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
Problem In a long, straight, vertical lightning stroke, electrons move downward and positive
ions move upward and constitute a current of magnitude 20.0 kA. At a location 50.0 m east of
the middle of the stroke, a free electron drifts through the air toward the west with a speed of
300 m/s.
a. Sketch showing the various vectors involved. Ignore the Earth’s magnetic field.
b. Find the vector force the lightning stroke exerts on the electron.
c. Find the radius of the electron’s path.
d. Is it a good approximation to model the electron as moving in a uniform field?
e. If it does not collide with any obstacles, how many revolutions will the electron complete
during the 60.0 s duration of the lightning stroke?
6
ORANGE COUNTRY
GO COWBOYS
PHYS 2114
LECTURE 14
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
7
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