EXERCISE C A wire carrying current I is perpendicular to a magnetic field of strength B . Assuming a fixed length of wire, which of the following changes will result in decreasing the force on the wire by a factor of 2? ( a ) Decrease the angle from 90° to 45°; ( b ) decrease the angle from 90° to 30°; ( c ) decrease the current in the wire to ( d ) decrease the magnetic field to ( e ) none of these will do it. B 2; I 2; The SI unit for magnetic field B is the tesla (T). From Eq. 20 – 1 or 20 – 2, we see that An older name for the tesla is the “weber per meter squared” Another unit sometimes used to specify magnetic field is a cgs unit, the gauss (G): A field given in gauss should always be changed to teslas before using with other SI units. To get a “feel” for these units, we note that the magnetic field of the Earth at its surface is about G or On the other hand, strong electromagnets can produce fields on the order of 2 T and superconducting magnets can produce over 10 T. 0.5 * 10 – 4 T. 1 2 1 G = 10 – 4 T. A 1 Wb m 2 = 1 T B . 1 T = 1 N A m. Magnetic force on a current-carrying wire. A wire carrying a steady (dc) 30-A current has a length between the pole faces of a magnet. The wire is at an angle to the field (Fig. 20 – 13). The magnetic field is approximately uniform at 0.90 T. We ignore the field beyond the pole pieces. Determine the magnitude and direction of the force on the wire. APPROACH We use Eq. 20 – 1, SOLUTION The force F on the 12-cm length of wire within the uniform field B is We use right-hand-rule-2 to find the direction of Hold your right hand flat, pointing your fingers in the direction of the current. Then bend your fingers (maybe needing to rotate your hand) so they point along Fig. 20 – 13. Your thumb then points into the page, which is thus the direction of the force F . B B , F B . = ( 30 A )( 0.12 m )( 0.90 T )( sin 60° ) = 2.8 N. F = I l B sin u F = I l B sin u . u = 60° l = 12 cm EXAMPLE 20 ; 1 EXERCISE D A straight power line carries 30 A and is perpendicular to the Earth’s mag- netic field of What magnitude force is exerted on 100 m of this power line? 0.50 * 10 – 4 T. On a diagram, when we want to represent an electric current or a magnetic field that is pointing out of the page (toward us) or into the page, we use or , respectively. The is meant to resemble the tip of an arrow pointing directly toward the reader, whereas the or resembles the tail of an arrow pointing away. See Fig. 20 – 14. z * * (toward viewer) 10.0 cm I I a b F B B B FIGURE 20–14 Measuring a magnetic field Example 20 – 2. B B . Measuring a magnetic field. A rectangular loop of wire hangs vertically as shown in Fig. 20 – 14. A magnetic field is directed horizontally, perpendicular to the plane of the loop, and points out of the page as represented by the symbol The magnetic field is very nearly uniform along the horizontal portion of wire ab (length ) which is near the center of the gap of a large magnet producing the field. The top portion of the wire loop is out of the field. The loop hangs from a balance (reads 0 when ) which measures a downward magnetic force of when the wire carries a current
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- Spring '14