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ch23_p3 - 3 We use = E dA and note that the side length of...

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3. We use Φ = z G G E dA and note that the side length of the cube is (3.0 m–1.0 m) = 2.0 m. (a) On the top face of the cube y = 2.0 m and ( ) ˆ j dA dA = G . Therefore, we have ( ) ( ) 2 ˆ ˆ ˆ ˆ 4i 3 2.0 2 j 4i 18j E = + = G . Thus the flux is ( ) ( ) ( )( ) 2 2 2 top top top ˆ ˆ ˆ 4i 18j j 18 18 2.0 N m C 72 N m C. E dA dA dA Φ = = = − = − = − ³ ³ ³ G G (b) On the bottom face of the cube y = 0 and dA dA G = b g e j # j . Therefore, we have E = + = 4 3 0 2 4 6 2 # # # # i j i j c h . Thus, the flux is ( ) ( ) ( ) ( ) 2 2 2 bottom bottom bottom ˆ ˆ ˆ 4i 6j j 6 6 2.0 N m C 24 N m C. E dA dA dA Φ = = = = = + ³ ³ ³ G G (c) On the left face of the cube ( ) ( ) ˆ i dA dA = G . So ( ) ( ) ( ) ( ) 2 2 2 left left bottom ˆ ˆ ˆ ˆ 4i j i 4 4 2.0 N m C 16 N m C. y E dA E dA dA Φ = = + = −
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