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# chap28 - 28.1 For a charge with velocity v(8.00 106 m s ^...

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28.1: For a charge with velocity , ˆ ) s m 10 8.00 ( 6 j v the magnetic field produced at a position r away from the particle is . ˆ 4 2 0 r q μ r v B So for the cases below: a) 4 1 2 0 , ˆ ˆ ˆ ˆ ) m 0.500 ( r k r v i r . ˆ ˆ ) T 10 1.92 ( ˆ ) m 0.50 ( ) s m 10 8.0 )( C 10 (6.0 4 ˆ 4 0 5 2 6 6 0 2 0 0 k k k k B B π μ r qv π μ b) . 0 0 ˆ ˆ ˆ ) m 0.500 ( B r v j r c) . 4 1 , ˆ ˆ ˆ ˆ ) m 0.500 ( 2 0 r i r v k r . ˆ ˆ 4 0 0 0 i i B 2 B r qv d) 0 2 2 2 1 , ˆ ˆ ˆ ˆ ) m 0.500 ( ˆ ) m 0.500 ( r r i r v k j r 2 2 ˆ 2 ˆ 2 2 ˆ 4 0 0 0 i B B r qv i i B 2 28.2: 2 2 0 total 4 d v q d qv B B B page. the into T, 10 38 . 4 ) m 120 . 0 ( ) s m 10 0 . 9 )( C 10 0 . 3 ( ) m 120 . 0 ( ) s m 10 5 . 4 )( C 10 0 . 8 ( 4 4 2 6 6 2 6 6 0 B μ B

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28.3: 3 0 4 r q π μ r v B a) ; ˆ , i r i v r v 0 , B 0 r v b) ; ˆ , ˆ j r i v r v m 0.500 , ˆ r vr k r v k B ˆ ) T 0 1.31 ( so negative, is T 10 1.31 ) m 0.500 ( ) s m 10 6.80 )( C 10 4.80 )( C s N 10 1 4 6 6 2 5 6 2 2 7 2 0 q r v q π μ B c) ); ˆ ˆ )( m 0.500 ( , ˆ j i r i v v m 0.7071 , ˆ ) m 0.500 ( r v k r v k B ˆ ) T 10 4.62 ( ; T 10 4.62 ) m 0.7071 ( ) s m 10 6.80 )( m 0.500 ( C) 10 4.80 )( C s N 10 1 4 7 7 3 5 6 2 2 7 3 0 B r r v q π μ B d) ; ˆ , ˆ k r i v r v m 0.500 , ˆ r vr j r v j B ˆ T) 10 1.31 ( ; T 10 1.31 m) 0.500 ( ) s m 10 6.80 )( C 10 4.80 )( C s N 10 1 4 6 6 2 5 6 2 2 7 2 0 B r v q π μ B 28.4: a) Following Example 28.1 we can find the magnetic force between the charges: down). points char lower the on force the and up points charge upper the on force (the N 10 1.69 ) m 0.240 ( m 10 9.00 )( s m 10 4.50 )( C 10 3.00 )( C 10 8.00 ( ) A m T 10 ( 4 3 2 6 6 6 6 7 2 0 r v v q q π μ F B The Coulomb force between the charges is N 3.75 ) C m N 10 8.99 ( 2 2 12 m) (0.240 C 10 0) (8.00)(3.0 2 2 9 2 2 1 r q q k F (the force on the upper charge points up and the force on the lower charge points down). The ratio of the Coulomb force to the magnetic force is 2 1 2 v v c 3 N 10 1.69 N 3.75 10 2.22 3 . b) The magnetic forces are reversed when the direction of only one velocity is reversed but the magnitude of the force is unchanged. 28.5: The magnetic field is into the page at the origin, and the magnitude is page. the into T, 10 1.64 m) 0.400 ( ) s m 10 8.0 )( C 10 1.5 ( ) m 0.300 ( ) s m 10 2.0 )( C 10 4.0 ( 4 4 6 2 5 6 2 5 6 0 2 2 0 B π B r v q r qv π μ B B B
28.6: a) 2 0 4 ; πd qv μ B q q q

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