329sp11hw1sol - D = A B = 4x 2y − 3z A B − 4C = 4x 2y...

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Unformatted text preview: D = A + B = 4x + 2y − 3z . A + B − 4C = 4x + 2y − 3z − 4 (x − 2y + 3z ) = 10y − 15z . |A + B − 4C| = 102 + 152 = 18.03. A + 2B − C = (3x + y − 2z ) + 2 (x + y − z ) − (x − 2y + 3z ) = 4x + 5y − 7z , |A + 2B − C| = u= ˆ 42 + 52 + 72 = 9.49, A + 2B − C 4x + 5y − 7z = = 0.42x + 0.53y − 0.74z . |A + 2B − C| 9.49 A · B = (3x + y − 2z ) · (x + y − z ) = 3 × 1 + 1 × 1 + (−2) × (−1) = 6. B × C = (x + y − z ) × (x − 2y + 3z ) = x × (x − 2y + 3z ) + y × (x − 2y + 3z ) − z ×(x −2y +3z ) = (−2z − 3y ) + (−z + 3x) − (y + 2x) = x − 4y − 3z . E F v F B F = q (E + v × B) 3z = E z = E+y × B 3z + 4y = E + 2z × B B = xBx + y By + z Bz E = 3z y × B = −2z z × B = 2y v , . y × (xBx + y By + z Bz ) = −2z z × (xBx + y By + z Bz ) = 2y . −z Bx + xBz = −2z y Bx − xBy = 2y Bx = 2 By = Bz =0 E = 3z (V/m) z=1 S1 J · dS = . B= 2x Wb/m2 S1 S 2 S3 S4 S 5 −x ˆ . S6 S1 1ˆ 1 ˆ 0 0 x=0 x=1 y=0 y=1 z=0 S1 S2 z 2 (x + y + z ) |x=0 · (−x) dydz = − 1 (A) . 3 +x S2 ˆ S2 ˆ J · dS = 0 S 3 S4 S5 S6 ˆ ˆ J · dS = S3 ˆ S4 ˆ S5 ˆ S6 1ˆ 1 0 1ˆ 1 z 2 (x + y + z ) |y=0 · (−y ) dxdz = − 1 (A) , 3 1 (A) , 3 J · dS = ˆ 1ˆ 1 z 2 (x + y + z ) |y=1 · (+y ) dxdz = J · dS = ˆ 1ˆ 1 z 2 (x + y + z ) |z =0 · (−z ) dxdy = 0 (A) , J · dS = ˆ 1ˆ 1 z 2 (x + y + z ) |z =1 · (+z ) dxdy = 1 (A) . 0 0 0 0 0 0 6 S Q1 1 (A) . 3 0 0 ˛ Q1 = 8πε0 z 2 (x + y + z ) |x=1 · (+x) dydz = J · dS = i=1 ˆ Si J · dS = 1 (A) . Q2 = −Q1 /2 = −4πε0 Q2 2 E3 = i=1 = = Qi r3 − ri · 2 |r − r | 4πε0 |r3 − ri | 3 i 2 1 (x + y ) − (−x + y ) 3 |x + y | | − x + y |3 3x + y √ (V/m) . 22 P3 P4 2 E4 = i=1 = = Qi r4 − ri · 2 |r − r | 4πε0 |r4 − ri | 4 i 2 1 (x + z ) − (−x + z ) 3 |x + z | | − x + z |3 3x + z √ (V/m) . 22 ...
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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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329sp11hw1sol - D = A B = 4x 2y − 3z A B − 4C = 4x 2y...

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