Magnetic Flux and Faraday’s Law of Induction
Answers to Even-numbered Conceptual Questions
The magnetic field indicates the strength and direction of the magnetic force that a
charged particle moving with a certain velocity would experience at a given point in
The magnetic flux, on the other hand, can be thought of as a measure of the
“amount” of magnetic field that passes through a given area.
The magnetic flux through the loop of wire is greatest when its normal points vertically
downward, because in this case the normal points in almost the same direction as the
There is little magnetic flux through the loop if its normal is horizontal;
that is, when its normal is essentially at right angles to the field.
When the disk is at its maximum displacement to the right, it is well within the region of
uniform magnetic field.
Therefore, the magnetic flux through the disk is not changing.
follows, then, that the induced current at this point is a minimum; namely, zero.
The magnetic field will have little apparent effect, because the break in the ring will
prevent a current from flowing around its circumference.
What the magnetic field will do,
however, is produce a nonzero emf between the two sides of the break.
In this case, the break prevents a current from circulating around the ring.
in turn, prevents the ring from experiencing a magnetic force that would propel it into the
The fact that the two wires are not connected means that no current can flow through
As a result, the magnetic field exerts zero force on the rod.
If the system is
frictionless, no force will be required to keep the rod moving with a constant speed.
As the penny begins to tip over, there is a large change in the magnetic flux through its
surface, due to the great intensity of the MRI magnetic field.
This change in magnetic
flux generates an induced current in the penny that opposes its motion.
As a result, the
penny falls over slowly, as if it were immersed in molasses.
Initially, the rod accelerates to the left, due to the downward current it carries.
speeds up, however, the motional emf it generates will begin to counteract the emf of the
Eventually the two emfs balance one another, and current stops flowing in the
From this point on, the rod continues to move with constant speed.
When the angular speed of the coil in an electric generator is increased, the rate at which
the magnetic flux changes increases as well.
As a result, the magnitude of the induced
emf produced by the generator increases.
Of course, the frequency of the induced emf
increases as well.
The energy stored in the inductor remains the same.
Doubling the number of turns per
length quadruples the inductance of the solenoid, as we can see from Equation 23-14.
energy stored in an inductor, however, depends on both the inductance of the inductor and
the current it carries, as we see in Equation 23-19.
In fact, the energy stored in an inductor
depends on the square of the current.