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class_9(Electrostatics_field)

class_9(Electrostatics_field) - EX 4.5 The finite sheet...

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EX 4.5 ) ( 2 x d xdx = ) ( 2 y d ydy = Use ) ( ) ( ) 25 ( 4 1 2 2 1 0 1 0 2 / 3 2 2 y d x d y x Q ∫ ∫ + + = dudv v u Q ∫ ∫ + + = 1 0 1 0 2 / 3 ) 25 ( 4 1 2 x u = 2 y v = Let nC Q 15 . 33 = Solution: (a). The total charge on the sheet (b). The electric field at (0,0,5) (c). The force experienced by a 1-mC charge located at (0,0,5) The finite sheet 0<x<1, and 0<y<1 on the z=0 plane has a charge density 2 2 / 3 2 2 / ) 25 ( m nC y x xy s + + = ρ Find: (a) dxdy y x xy Q ∫ ∫ + + = 1 0 1 0 2 / 3 2 2 ) 25 (

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EX 4.5 (a). The total charge on the sheet (b). The electric field at (0,0,5) (c). The force experienced by a 1-mC charge located at (0,0,5) The finite sheet 0<x<1, and 0<y<1 on the z=0 plane has a charge density 2 2 / 3 2 2 / ) 25 ( m nC y x xy s + + = ρ Find: Solution: (b). Coulomb's law: R R dQ E d d 3 0 4 1 πε = dxdy dS dQ s s ρ ρ = = ) 0 , , ( ) 5 , 0 , 0 ( y x R - = ) 5 , , ( y x - - = 2 / 1 2 2 ) 25 ( + + = y x R ) 5 , , ( ) 25 ( 4 1 2 / 3 2 2 0 y x y x dxdy E d s - - + + = ρ πε
EX 4.5 (a). The total charge on the sheet (b). The electric field at (0,0,5) (c). The force experienced by a 1-mC charge located at (0,0,5) The finite sheet 0<x<1, and 0<y<1 on the z=0 plane has a charge density 2 2 / 3 2 2 / ) 25 ( m nC y x xy s + + = ρ Find: Solution: (b). ) 5 , , ( ) 25 ( ) 25 ( 4 1 2 / 3 2 2 2 / 3 2 2 0 y x y x dxdy y x xy E d - - + + + + = πε xydxdy y x E d ) 5 , , ( 4 1 0 - - = πε ∫ ∫ = s E d E ∫ ∫ - - = 1 0 1 0 0 ) 5 , , ( 4 1 xydxdy y x πε m V / ) 25 . 11 , 5 . 1 , 5 . 1 ( - - =

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EX 4.5 (a). The total charge on the sheet (b). The electric field at (0,0,5) (c). The force experienced by a 1-mC charge located at (0,0,5) The finite sheet 0<x<1, and 0<y<1 on the z=0 plane has a charge density 2 2 / 3 2 2 / ) 25 ( m nC y x xy s + + = ρ Find: Solution: (C).
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class_9(Electrostatics_field) - EX 4.5 The finite sheet...

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