Homework 6 Solutions Phys 2B
Dr. Stolovy
Ch. 20 Problems: 3, 7, 9, 12, 15, 18, 32, 39, 43, 49
20.3
, where is the angle between the direction of the field and the
normal to the plane of the loop.
(a) If the field is perpendicular to the plane of the loop,
, and
(b) If the field is directed parallel to the plane of the loop,
20.7
, and
(a) The magnetic flux through an area A may be written as
Thus, the flux through the shaded side of the cube is
(b) Unlike electric field lines, magnetic field lines always form closed loops, without
beginning or end. Therefore, no magnetic field lines originate or terminate within
the cube and any line entering the cube at one point must emerge from the cube at
some other point. The net flux through the cube, and indeed through any closed
surface, is
20.9
(a) As loop A moves parallel to the long straight wire, the magnetic flux through loop
A does not change. Hence, there is
in this loop.
(b) As loop B moves to the left away from the straight wire, the magnetic flux through
this loop is directed out of the page, and is decreasing in magnitude. To oppose this
change in flux, the induced current flows
producing a
magnetic flux directed out of the page through the area enclosed by loop B.
(c) As loop C moves to the right away from the straight wire, the magnetic flux through
this loop is directed into the page and is decreasing in magnitude. In order to oppose
this change in flux, the induced current flows
producing a
magnetic flux directed into the page through the area enclosed by loop C.
20.12
With the field directed perpendicular to the plane of the coil, the flux through the coil is
. As the magnitude of the field decreases, the magnitude of the induced
emf in the coil is
20.15
(a) When the magnet moves to the left, the flux through the interior of the coil is
directed toward the right and is decreasing in magnitude. To oppose this change in
flux, 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
through the
resistor.
(b) When the magnet moves to the right, the flux through the interior of the coil is
directed toward the right and is increasing in magnitude. To oppose this increasing
flux, the magnetic field generated by the induced current should be directed toward
the left along the axis of the coil. The current must then be
through the
resistor.
20.18
The initial magnetic field inside the solenoid is
(a)
(b) When the current is zero, the flux through the loop is
induced emf has been
20.32
20.39
and the average
Note that the vertical component of the magnetic field is always parallel to the plane of
the coil, and can never contribute to the flux through the coil. The maximum induced
emf in the coil is then
From
we have
20.43
(a) In the series circuit of Figure P20.43, maximum current occurs after the switch has
been closed for a very long time, when current has stabilized and the back emf due
to the inductance has decreased to zero. This maximum current is given by
(b) The time constant of the RL circuit is
(c) If the switch in the RL circuit is closed at time
is given by
Thus,
or
With
will be
at time
20.49
(a) The energy stored by an inductor is
(b) If
the stored energy will be
the current as a function of time
the current in this circuit
so the self inductance is