Chapter Review
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Chapter 22: Magnetism Chapter Review |
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Chapter Review
22-1 The Magnetic Field
Some materials are almost always magnetic as a direct result of their structure; objects made of these materials are called permanent magnets. The prototype object for discussing the behavior of these materials is the simple bar magnet. The two ends of a bar magnet behave differently. One end, the north pole of the magnet tends to point northward with respect to the earth. The other end, the south pole of the magnet tends to point southward. Magnets always have both a north and a south pole. There is a force between two magnets. The basic behavior of this force is reminiscent of the force between two charges:
like magnetic poles repel, opposite poles attract.
As with electricity, a magnet produces a magnetic field, for which we use the vector symbol B. Magnetic field lines can be drawn to get a visual representation of this field. In order to draw magnetic field lines, we must know how to determine the direction of the magnetic field. The rule for the direction of B is the following:
The direction of the magnetic field at a given location is the direction that the north pole of a compass needle would point if placed at that location.
With the above definition, we can now state the rules for drawing magnetic field lines:
(1) Magnetic field lines are tangent to the magnetic field at every point;
(2) Magnetic field lines point away from the north pole of a magnet and toward its south pole;
(3) The number of magnetic field lines is proportional to the magnitude of the field;
(4) Magnetic field lines always form closed loops.
See figure 22-4 of the text for an example of magnetic field lines.
The fact that bar magnets interact with Earth is evidence that Earth has a magnetic field. The poles of Earth's magnetic field are near to Earth's geographic poles. However, the definition of the magnetic poles and how they behave requires that the magnetic pole of the earth that's near to Earth's north pole (called the north magnetic pole) is actually the south pole of Earth's magnetic field. Similarly, the magnetic pole of the earth that's near to Earth's south pole (called the south magnetic pole) is actually the north pole of Earth's magnetic field (See figure 22-6 of the text).
Physlet Illustration: Magnetic Field of a Bar Magnet | |
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| In this simulation, a bar magnet is shown. A compass (whose needle points "north") may be dragged around in the plane of the screen. Can you map the lines of the magnetic field due to the magnet? | |
Hints:
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Practice Quiz
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22-2 The Magnetic Force on Moving Charges
In addition to the behavior described above, magnets also apply a force to charged objects that are moving through the magnetic field. The magnitude of the force on this charge depends on the magnitude of the charge q, the magnitude of its velocity v, the magnitude of the magnetic field B, and the smallest angle q between the vectors B and v:
F = qvBsin q.
Notice that if q = 0o (or 180o), that is, if the charge moves in the direction of the magnetic field, the force on it is zero. Therefore, a force is exerted only if the velocity of the charge has a component perpendicular to the magnetic field.
The above expression for the force on a moving charge can be used to obtain the magnitude (or strength) of the magnetic field
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This relation shows that the SI units of the magnetic field can be derived from N/(C.m/s). After some rearranging, these units can be written as N/(A.m) which is called a tesla (T): 1 T = 1 N/(A.m).
The direction of the force on a moving charge is found to be perpendicular to both B and v. That is, F is perpendicular to the plane formed by the vectors B and v. However, this statement still leaves two possible directions for F on either side of the B-v plane. To determine the direction of F more precisely we use the magnetic force right-hand-rule:
To find the direction of the magnetic force on a positive charge, point the fingers of your right hand in the direction of v. Orient your hand such that your fingers can curl toward the direction of B. Your thumb then indicates the direction of F. If the charge is negative, the force points in the opposite direction indicated by your thumb.
Essentially, the above rule determines on which side of the B-v plane F points; since you know F must be perpendicular to this plane, then you know the precise direction of F.
The magnetic force on a moving charge is necessarily a three-dimensional situation. On two-dimensional sheets of paper this involves the directions directly into the page and out of the page. These directions are indicated by using the symbol 
for into the page, and 
for out of the page.
Example 22.1 Force on a Moving Charge: The magnetic field in a region is 
. An object of charge -1.7 C moves into this region with a velocity of v = (4.5 m/s)
. Determine the magnitude and direction of the force on this charge.
Picture the Problem The picture shows the magnetic field and velocity vectors.
Strategy From the components given, it is clear that B makes a 45o angle in the 1st quadrant. With this insight we can proceed using the expression for the force.
Solution
| 1. The magnitude of B is: |  |
| 2. The magnitude of the force is: | F = qvBsin q = (1.7 C)(4.5 m/s)(3.54 m/s)sin(45o) = 19 N |
| 3. The right-hand rule gives the direction as: | into the page, |
Insight Only the magnitude of the charge was used to get the magnitude of the force as appropriate. Also, make sure you recognize that because the charge is negative, the direction of the force is opposite to the direction indicated by your thumb when you use the magnetic force right-hand rule.
Practice Quiz
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