Unformatted text preview: e induced field, therefore, must be into the paper. The current
in the coil must be clockwise .
b. At position 2 the magnetic field is directed into the paper and is decreasing as the coil
moves away from the wire. The induced magnetic field, therefore, must be directed into the
paper, so the current in the coil must be clockwise . ______________________________________________________________________________
36. REASONING According to Lenz’s law, the induced current in the triangular loop flows in
such a direction so as to create an induced magnetic field that opposes the original flux
change.
SOLUTION
a. As the triangle is crossing the +y axis, the magnetic flux down into the plane of the paper
is increasing, since the field now begins to penetrate the loop. To offset this increase, an
induced magnetic field directed up and out of the plane of the paper is needed. By applying
RHR2 it can be seen that such an induced magnetic field will be created within the loop by a
counterclockwise induced current .
b. As the triangle is crossing the −x axis, there is no flux change, since all parts of the
triangle remain in the magnetic field, which remains constant. Therefore, there is no induced
magnetic field, and no induced current appears .
c. As the triangle is crossing the −y axis, the magnetic flux down into the plane of the paper
is decreasing, since the loop now begins to leave the field region. To offset this decrease, an
induced magnetic field directed down and into the plane of the paper is needed. By applying
RHR2 it can be seen that such an induced magnetic field will be created within the loop by a
clockwise induced current . Chapter 22 Problems 1215 d. As the triangle is crossing the +x axis, there is no flux change, since all parts of the
triangle remain in the fieldfree region. Therefore, there is no induced magnetic field, and
no induced current appears . 37. REASONING The current I in the straight wire produces
Table top
Region 1
a circular pattern of magnetic field lines around the wire.
The magnetic field at any point is tangent to one of these
circular field lines. Thus, the field points perpendicular to
I
the plane of the table. Furthermore, according to RightHand Rule No. 2, the field is directed up out of the table
surface in region 1 above the wire and is directed down
Region 2
into the table surface in region 2 below the wire (see the
drawing at the right). To deduce the direction of any induced current in the circular loop, we
consider Faraday’s law and the change that occurs in the magnetic flux through the loop due
to the field of the straight wire.
SOLUTION As the current I decreases, the magnitude of the field that it produces also
decreases. However, the directions of the fields in regions 1 and 2 do not change and remain
as discussed in the reasoning. Since the fields in these two regions always have opposite
directions and equal magnitudes at any given radial distance from the straight wire, the flux
through the regions add up to give zero for any value of the current. With the flux remaining
constant as time passes, Faraday’s law indicates that there is no induced emf in the coil.
Since there is no induced emf in the coil, there is no induced current .
______________________________________________________________________________
38. REASONING AND SOLUTION If the applied magnetic field is decreasing in time, then
the flux through the circuit is decreasing. Lenz's law requires that an induced magnetic field
be produced which attempts to counteract this decrease; hence its direction is out of the
paper. The sense of the induced current in the circuit must be CCW. Therefore, the lower
plate of the capacitor is positive while the upper plate is negative. The electric field between
the plates of the capacitor points from positive to negative so the electric field points
upward .
______________________________________________________________________________
39. REASONING AND SOLUTION
a. Location I
As the loop swings downward, the normal to the loop makes a smaller angle with the
applied field. Hence, the flux through the loop is increasing. The induced magnetic field
must point generally to the left to counteract this increase. The induced current flows x→y→z 1216 ELECTROMAGNETIC INDUCTION Location II
The angle between the normal to the loop and the applied field is now increasing, so the flux
through the loop is decreasing. The induced field must now be generally to the right, and
the current flows
z→ y→ x
b. Location I
The argument is the same as for location II in part a. z→ y→ x
Location II
The argument is the same as for location I in part a. x→y→z
______________________________________________________________________________
40. REASONING When the motor is running at normal speed, the current is the net emf
divided by the resistance R of the armature wire. The net emf is the applied voltage V minus
the back emf developed by the rotating coil. We can use this relation to find the back e...
View
Full Document
 Spring '13
 CHASTAIN
 Physics, Pythagorean Theorem, Force, The Lottery, Right triangle, triangle

Click to edit the document details