AP Physics C 2017

the electric field. By the time it gets to the end of the electric field, it has acquired a high velocity, which
can be calculated using conservation of energy. Then the particle travels through a tiny opening and enters
a uniform magnetic field. This magnetic field exerts a force on the particle, and the particle begins to
travel in a circle. It eventually hits the wall that divides the electric-field region from the magnetic-field
region. By measuring where on the wall it hits, you can determine the radius of the particle’s path.
Plugging this value into the equation we derived for the radius of the path, you can calculate the particle’s
mass r = mv/qB .
You may see a problem on the free-response section that involves a mass spectrometer. These
problems may seem intimidating, but, when you take them one step at a time, they’re not very difficult.

Induced EMF

A changing magnetic field produces a current. We call this occurrence electromagnetic induction .
So let’s say that you have a loop of wire in a magnetic field. Under normal conditions, no current
flows in your wire loop. However, if you change the magnitude of the magnetic field, a current will begin
to flow.
We’ve said in the past that current flows in a circuit (and a wire loop qualifies as a circuit, albeit a
simple one) when there is a potential difference between the two ends of the circuit. Usually, we need a
battery to create this potential difference. But we don’t have a battery hooked up to our loop of wire.
Instead, the changing magnetic field is doing the same thing as a battery would. So rather than talking
about the voltage of the battery in this circuit, we talk about the “voltage” created by the changing
magnetic field. The technical term for this “voltage” is induced EMF .

Induced EMF :   The potential   difference  created by  a   changing    magnetic    field   that    causes  a   current to

flow    in  a   wire.   EMF stands  for Electro-Motive  Force,  but is  NOT a   force.

For a loop of wire to “feel” the changing magnetic field, some of the field lines need to pass through it.
The amount of magnetic field that passes through the loop is called the magnetic flux . This concept is
pretty similar to electric flux.

Magnetic    Flux    :   The number  of  magnetic    field   lines   that    pass    through an  area

The units of flux are called webers; 1 weber = 1 T·m^2 . The equation for magnetic flux is

In this equation, Φ (^) B is the magnetic flux, B is the magnitude of the magnetic field, and A is the area of the
region that is penetrated by the magnetic field.
Let’s take a circular loop of wire, lay it down on the page, and create a magnetic field that points to
the right, as shown in Figure 20.9 .