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Unformatted text preview: Chapter 27 Sources of the Magnetic Field Conceptual Problems 1 • Sketch the field lines for the electric dipole and the magnetic dipole shown in Figure 27-47. How do the field lines differ in appearance close to the center of each dipole? Picture the Problem Note that, while the two far fields (the fields far from the dipoles) are the same, the two near fields (the fields near to the dipoles) are not. At the center of the electric dipole, the electric field is antiparallel to the direction of the far field above and below the dipole, and at the center of the magnetic dipole, the magnetic field is parallel to the direction of the far field above and below the dipole. It is especially important to note that while the electric field lines begin and terminate on electric charges, the magnetic field lines are continuous, i.e., they form closed loops. 2 • Two wires lie in the plane of the page and carry equal currents in opposite directions, as shown in Figure 27- 48. At a point midway between the wires, the magnetic field is ( a ) zero, ( b ) into the page, ( c ) out of the page, ( d ) toward the top or bottom of the page, ( e ) toward one of the two wires. Determine the Concept Applying the right-hand rule to the wire to the left we see that the magnetic field due to its current is out of the page at the midpoint. Applying the right-hand rule to the wire to the right we see that the magnetic field due to its current is also out of the page at the midpoint. Hence, the sum of the magnetic fields is out of the page as well. 1is correct. 3 • Parallel wires 1 and 2 carry currents I 1 and I 2 , respectively, where I 2 = 2 I 1 . The two currents are in the same direction. The magnitudes of the magnetic force by current 1 on wire 2 and by current 2 on wire 1 are F 12 and F 21 , respectively. These magnitudes are related by ( a ) F 21 = F 21 , ( b ) F 21 = 2 F 12 , ( c ) 2 F 21 = F 12 , ( d ) F 21 = 4 F 12 , ( e ) 4 F 21 = F 12 . Determine the Concept While we could express the force wire 1 exerts on wire 2 2563 Chapter 27 2564 and compare it to the force wire 2 exerts on wire 1 to show that they are the same, it is simpler to recognize that these are action and reaction forces. ) ( a is correct. 4 • Make a field-line sketch of the magnetic field due to the currents in the pair of identical coaxial coils shown in Figure 27-49. Consider two cases: ( a ) the currents in the coils have the same magnitude and have the same direction and ( b ) the currents in the coils have the same magnitude and have the opposite directions. Picture the Problem ( a ) The field-line sketch follows. An assumed direction for the current in the coils is shown in the diagram. Note that the field is stronger in the region between the coaxial coils and that the field lines have neither beginning nor ending points as do electric-field lines. Because there are an uncountable infinity of lines, only a representative few have been shown....
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- Summer '08