P32_028 - 28. (a) Noting that the magnitude of the electric...

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28. (a) Noting that the magnitude of the electric Feld (assumed uniform) is given by E = V/d (where d =5 . 0 mm), we use the result of part (a) in Sample Problem 32-3 B = µ 0 ε 0 r 2 dE dt = µ 0 ε 0 r 2 d dV dt (for r R ) . We also use the fact that the time derivative of sin( ωt )(where ω =2 πf π (60) 377/s in this problem) is ω cos( ). Thus, we Fnd the magnetic Feld as a function of r (for r R ; note that this neglects “fringing” and related e±ects at the edges): B = µ 0 ε 0 r 2 d V max ω cos( )= B max = µ 0 ε 0 rV max ω 2 d where V max = 150 V. This grows with r until reaching its highest value at r = R = 30 mm: B max ¯ ¯ ¯ ¯ r = R = µ 0 ε 0 RV max ω 2 d = ( 4 π × 10 7 H / m )( 8 . 85 × 10 12 ² / m 30 × 10 3 m ) (150 V)(377 / s) 2(5 . 0 × 10 3 m) =1 . 9 × 10 12 T . (b) ²or r 0 . 03 m, we use the B max = µ 0 ε 0 rV max ω 2 d expression found in part (a) (note the
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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