Solutions to Homework Questions 6

Physics 112 Homework 6 (solutions) (2004 Fall)
Chapt20, Problem-17: The person in Figure P20.17 is girded
about the chest with a breathing monitor, which is a 100-turn coil. As a breath
is inhaled, the area of the coil varies from 0.120 m 2 to 0.124 m 2 . Earth’s
magnetic field is 50.0 _T and makes an angle of 22.5° with respect to the
normal to the loop. If the patient inhales a breath in 1.59 s, what is the
average voltage induced in the coil during the inhalation
Solution:
( )
! = N "# B NB ("A)cos$
=
"t "t
= 100 ( 50.0 ! 10-6 T) [( 0.124 " 0.120) m 2
]cos 22.5°
1.59 s
= 1.16 !10 "5 V= 11.6 µV
Chapt20, Problem-19: A Boeing-747 jet with a wing span of 60.0 m is flying horizontally at a speed of
300 m/s over Phoenix, Arizona, at a location where Earth’s magnetic field is 50.0 µT at 58.0° below the horizontal. What
voltage is generated between the wingtips
Solution:
! = B " l v , where B ! is the component of the magnetic field perpendicular to the velocity v. Thus,
( ) 300 m s
[ ] 60.0 m
! = ( 50.0 " 10 #6 T)sin 58.0°
( )= 0.763 V
Chapt20, Problem-22: A helicopter has blades of length 3.0 m, rotating at 2.0 rev/s about a central hub. If
the vertical component of Earth’s magnetic field is 5.0x10 –5 T, what is the emf induced between the blade tip and the central
hub
Solution:
During each revolution, one of the rotor blades sweeps out a horizontal circular area of radius l, A = ! l 2 .
The number of magnetic field lines cut per revolution is !" B = B # A = B vertical A. The induced emf is then
! = "# B
"t
( )
= B vertical
$ l 2
1 f
( ) $ 3.0 m
= 5.0 %10 &5 T
0.50 s
[ ( ) 2
]
= 2.8 % 10 &3 V =
2.8 mV
Chapt20, Problem-23: A bar magnet is positioned near a coil
of wire as shown in Figure P20.23. What is the direction of the current through
the resistor when the magnet is moved (a) to the left (b) to the right
Solution:
(a) To oppose the motion of the magnet, the magnetic field generated
by the induced current should be directed to the right along the axis of
the coil. The current must then be left to right through the resistor.
(b) The magnetic field produced by the current should be directed to
the left along the axis of the coil, so the current must be right to left
through the resistor.
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