Homework Helpers: Physics

7 Magnetism

In a story that is often told as if it were the very definition of the word serendipitous, Danish physicist Hans Christian Oersted (1777–1851) discovered evidence of the relationship between electricity and magnetism, which would eventually become understood to be a unified force. As the story goes, he completed a simple circuit on his lab table and noticed that it caused the deflection of a nearby compass. With this simple observation, he realized that electric current could affect the motion of magnets. Further studies showed that the compass needle would move when the current was turned on, and again when it was turned off. A current-carrying wire is surrounded by a magnetic field. Electricity produces magnetism.

Figure 7.2

It is possible to use iron filings and a compass to map out the magnetic field surrounding a current-carrying wire. If you poke a straight, current-carrying wire through a white piece of paper and sprinkle iron filings on the paper, a pattern of concentric circles forms around the wire. Using the compass, you could determine whether the magnetic field is clockwise or counterclockwise.

Because a compass is not always handy on the day of a test, something called the “right-hand rule” has been developed to determine what the direction of the magnetic field around a current-carrying wire would be.

Before we go over the right-hand rule, let”s go over a convention that is used to deal with the fact that, although magnetic fields are three-dimensional, our drawings that are meant to represent magnetic fields are only in two dimensions. We can use arrows to represent directions that are to the left, right, top, or bottom of our page, but we need symbols to show fields or objects that are directed toward us or away from us, meaning “into the page” or “out of the page” we are reading.

The logic behind the choice of these particular symbols will help you remember which is which. We always use arrows to indicate direction. If an arrow were headed toward you, out of the page, you would see the point of the arrowhead, which might look like our dot symbol. If the arrow were headed away from you, into the page, you would see the back of the feathers, which might look something like our X symbol.

Figure 7.3

Now, here are the directions for applying the right-hand rule to current-carrying wires.

1. Point the thumb of your right hand in the direction of the conventional (+) current. If the picture shows the direction of the electron flow, point your thumb in the opposite direction.

2. Allow the other four fingers of your right hand to curl. They will curl in the direction of the magnetic field around the wire.

Let”s try some examples of applying the right-hand rule, which incorporates our two new symbols.

Example 1

Use the right-hand rule to determine the direction of the magnetic field around the current-carrying wire in Figure 7.4.

Step 1: Point the thumb of your right hand in the direction of the conventional (+) current. If the picture shows the direction of the electron flow, point your thumb in the opposite direction.

The X symbol indicates that the conventional current is directed into the page. Therefore, point your thumb into the page.

Figure 7.4

Step 2: Allow the other four fingers of your right hand to curl. They will curl in the direction of the magnetic field around the wire.

Your remaining fingers should be curling in a clockwise direction.

Answer: The magnetic field around the wire is in a clockwise direction.

If you were asked to sketch the field on the diagram, it should look like Figure 7.5.

Figure 7.5

Example 2

Use the right-hand rule to determine the direction of the magnetic field around the current-carrying wire in Figure 7.6.

Figure 7.6

Step 1: Point the thumb of your right hand in the direction of the conventional (+) current. If the picture shows the direction of the electron flow, point your thumb in the opposite direction.

The electron (–) flow is to the right, so point your thumb to the left side of the page.

Step 2: Allow the other four fingers of your right hand to curl. They will curl in the direction of the magnetic field around the wire.

Your remaining fingers should be curling toward the page. If you imaging grabbing the wire with your hand, you will see that the magnetic field will be directed into the page above the wire, and out of the page below the wire. This is easier to show with a picture than it is to explain with words.

Figure 7.7

Magnetic Fields Around Solenoids

If you ever constructed an electromagnet, you probably recall wrapping a wire several times around a piece of metal, such as a nail. When you make a coil of wires such as this, it is called a solenoid. The nail would act as the core of the electromagnet. When current is sent through the solenoid, the magnetic fields of the individual wire loops work together to produce a stronger magnetic field around the solenoid. The solenoid will act like a bar magnet, developing a north pole and a south pole. The right-hand rule can be used to determine the direction of the magnetic field and the identity of the induced poles.

1. Figure out the direction of the conventional current through the front of one of the wire loops.

2. Point the thumb of your right hand in the direction of the conventional current.

3. When the other fingers are held out straight, and at right angles to your thumb, they will be pointing towards the south pole of the magnetic field.

4. If you curl the other fingers of your right hand (not your thumb) they will show the direction of the magnetic field through the center of the solenoid and point toward the north pole of the magnetic field.

Lesson 7–2 Review

1. In what direction do the magnetic field lines point inside a solenoid?

2. A wire is orientated “into the page” with the conventional current coming “out of the page,” or toward you. What is the direction of the magnetic field (clockwise or counterclockwise) around the wire?

3. Imagine a current-carrying wire with the conventional current directed from left to right. Would the magnetic field be directed into or out of the page directly below (not behind) the wire?