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Another Way to Change Flux
In the previous lesson, we defined the magnetic flux (ΦB) through a coil of wire as the product of three quantities. We calculated flux by multiplying the (1) magnetic field, (2) area, and (3) cosine of the angle between the magnetic field and the area vector. In other words:
We also saw that
Faraday’s Law states that the induced emf in the coil of wire depends on the rate of change of this magnetic flux. Since there are three quantities that contribute to the flux, changing any one of these over time would induce an emf in the coil. In the
previous lesson we considered cases where we changed the flux by changing either the magnetic field strength or by changing the area over time. In this lesson, let’s consider changing the flux by changing the angle between the area vector and the magnetic field. In other words, let’s cause the coil of wire to
rotate within the magnetic field. This is most commonly done in a
generator.
Consider a horseshoe magnet with a square loop of wire in the magnet’s field. Now imagine that we attach a handle to one side of the loop that allows us to rotate the wire between the poles of the magnet. Points “A” and “B” on the loop are simply marked for reference. We can see that, when the loop is in Position 1, there is no flux through the loop.
As the loop is rotated from Position 1 to Position 2 over time, however, we notice that there is an increasing flux through loop. In addition, as the handle turns the loop from Position 2 to Position 3, the flux through the loop is now decreasing with time. As we continue to turn the handle at a constant angular speed through one full rotation (through Position 5), we see that not only does the flux change with time but that the rate of change of flux varies as well. Faraday’s Law reminds us that this rate of change of flux leads to the induced emf in the loop. For parts of the rotation the emf—and thus the current—points from B → A (in a clockwise (CW) direction when viewed from right). For other parts of the rotation, the emf and current point from A → B (in the counterclockwise (CCW) direction when viewed from right). We see this for several different positions below. The graphs illustrate the flux, rate of change in flux, and induced emf (and current) as a function of time.
Even though the loop rotates with a constant angular speed, we observe that the rate of change in flux is not constant. In fact, the second graph above illustrates that it follows the shape of a cosine function over a complete cycle. We can see why this is true by considering the loop at a location halfway between Position 1 and 2—when it has rotated 45o. Notice that the flux in this position is actually more than half the value of the flux at 90o. In other words, the flux changes quicker from 0 o to 45 o than it does from 45 o to 90 o. From the second graph above, we can see that the rate of change of flux is greatest when the slope of the flux vs. time graph (the first graph) is the steepest. In fact, the slope of the flux vs. time graph is, by definition, the rate of change of flux. It follows then that the induced emf and current (the third graph) will vary with time and even change directions partway through the cycle.
Simply by turning the handle, we’ve generated electricity. We could have, however, used falling water to provide the force needed to turn the loop of wire. We could have used wind power to spin blades that are connected to the loop. We could have even used high pressure steam that was heated by burning coal, natural gas or by a nuclear reaction to turn the loop. Sounds far-fetched? Not at all. This is how we actually generate electricity—the electricity that charges your cell phone, runs your refrigerator, and is evening powering your computer right now. In the next two sections we’ll explore just how the electricity actually makes it from the power plant to your electronic devices. What you’ve just uncovered above, however, is the physics behind how we generate electricity!
A Motor in Reverse
The components of a generator that we’ve just explored look remarkably similar to the electric motor that we studied in the previous chapter. In fact, you can think of a generator as an electric motor in reverse. While the motor uses electricity to get something spinning, a generator uses something spinning to generator electricity. You may have even realized that a motor can become a generator by mechanically spinning the shaft connected to the rotating loop of wire.
| |
Motor |
Generator |
| Input |
Electricity |
Mechanical Motion |
| Output |
Mechanical Motion |
Electricity |
In a real motor or generator, you’ll find that rather than having a single loop that rotates, there are often hundreds of loops that rotate. This makes sense in terms of the magnetic force equation that makes a motor spin. For every loop of wire, the length of wire L that is in the magnetic field increases. This makes the magnetic force which spins the loop grow proportionally as well. This also makes sense for a generator when we consider Faraday’s Law. The magnitude of the induced emf depends on the number of loops, N. So, a ‘strong’ motor will also be an effective generator.
| Motor |
Generator |
| F=I L B⊥ |
 |
In our generator above, we kept the magnet stationery and rotated the loop of wire. You may have wondered if it is possible to generate electricity using a stationary loop and a rotating magnet instead. The answer is yes. In fact, some generators are made where the magnet is the thing that is spinning and the loop is fixed in space. This offers some advantages in terms of efficiency, reliability, and maintenance, especially for large-scale power generation. Either way, the critical component is a changing magnetic flux through a wire loop.
Alternating Current
We saw above that when a wire loop spins in a magnetic field it induced a clockwise current (from B → A) for half of its rotation and counterclockwise current (from A → B) for the other half. In other words, the current alternates. It’s probably no surprise that we call this alternating current. The wall outlets in your home supply alternating current to the electrical cord that you plug into them. This is different for batteries, however. Batteries supply direct current. Direct current means the current only flows in one direction through the circuit. Since you use many devices that run on batteries—cell phones, laptops, and rechargeable watches, to name a few—why don’t we just have wall outlets supply direct current? Wouldn’t that be easier? One of the main reasons is what we saw above. Like it or not, alternating current is what gets generated when we have a loop of wire spinning in a magnetic field. Whenever we generate electricity, we produce alternating current. That’s where alternating current comes from in the first place!
There are other advantages to using alternating current, however. Another reason is because alternating current is easier to step-up or step-down in voltage. A wall outlet’s 120 V potential difference is too large for your cell phone’s 5 V charger. This brings us to a critical component in understanding how electricity is transmitted. What is this critical component? That’s what we’ll investigate in the next section!
Check Your Understanding
1. A generator can be described as a motor in reverse. Select TWO statements that illustrate why this is true.
(A) A motor requires motion to produce electric current.
(B) A motor requires electric current to produce motion.
(C) A generator requires motion to produce electric current.
(D) A generator requires electric current to produce motion.
2. Is it possible to make a generator with a spinning magnet and a stationary wire loop rather than a spinning loop and a stationary magnet?
3. A side view shows the end segment of a rectangular wire loop placed between the poles of a horseshoe magnet. Three positions of the wire loop are shown as it rotates in the magnetic field. Rank (from smallest to greatest) the magnetic flux through the loop for these three positions:
4. The graph below shows the flux through a wire loop as a function of time.
Which of these graphs best illustrates the rate of change in flux as a function of time for this same loop?
5. Two generators (one red and one purple) have identical wire loops that spin in identical magnetic fields. The only difference is that they spin at different rates. Their flux vs. time graph is shown below:
Which generator will produce the greatest maximum induced current?
(A) The red generator
(B) The purple generator
(C) Both produce the same maximum induced current
6. Two generators (one red and one purple) have identical wire loops that spin in identical magnetic fields. The only difference is that they spin at different rates. Their flux vs. time graph is shown below.
Which will produce a higher frequency alternating current?
(A) The red generator
(B) The purple generator
(C) The frequency would be the same in both generators
7. The magnetic flux through a loop in a generator is shown to the right. The flux values at four different times throughout a cycle have been labeled. Rank (from smallest to greatest) the magnitude of the induced current at these four instances.
8. The magnetic flux through a loop in a generator is shown to the right. The flux values at four different times throughout a cycle have been labeled. At what other instances would the induced current point in the same direction as it does at ‘b’?