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HW04Sol - Jim Guinns PHYS2212 Assignment#4 Solutions 1...

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Jim Guinn’s PHYS2212 Assignment #4 Solutions 1. Consider a uniform electric field, = (2.00kN/C) . a) What is the flux of this field through a square of side 10.0cm in plane parallel to the y- z plane? Since the electric field is uniform over the area of the square, the flux is given by Φ = · = E A = (2.00x10 3 N/C) (10.0x10 -2 m) 2 = Φ = 20.0N m 2 /C b) What is the flux through the same square if the normal to its plane makes a 30.0 o angle with the x-axis? In this case Φ = · = E A cos30.0 o = (2.00x10 3 N/C) (10.0x10 -2 m) 2 cos30.0 o = Φ = 17.3N m 2 /C . 2. An electric field is = (200.N/C) for x > 0 and = (-200.N/C) for x < 0 . A cylinder of length 20.0cm and radius 5.00cm has its center at the origin and its axis along the x-axis such that one end is at x = 10.0cm and the other is at x = -10.0cm. a) What is the flux through each end? Each end of the cylinder has its outward normal pointing along the field direction; hence, Φ = E A = E ( π r 2 ) = (200.N/C) π (0.0500m) 2 = Φ = 1.57N m 2 /C . b) What is the flux through the curved surface of the cylinder? The outward normal to the curved surface is always perpendicular to the electric field, so
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