Two infinite planes of charge lie parallel to each other and to the xy plane. Th

Question

Two infinite planes of charge lie parallel to each other and to the xy plane. The bottom plate located at z = 0 has surface charge density sigma h = - 3.5 mu C/m2 and the top plate located at z = + 2.0 m has surface charge density sigma 1, = + 6.0 mu C/m2. What is the electric field at some point P between the two plates? A small charged particle (m = 0.50 grams and q = - 0.5 mu C) is placed initially at rest at z = + 0.5 m between the two plates. Clearly the charged particle accelerates towards one of the plates. Which plate does the particle hit? What is the velocity of the particle when it hits the plate?

Explanation / Answer

b = -3.5C/m2, t = 6.0C/m2, z = 2.0 m, m = 0.50 g, q = -0.5 C,zo = 0.5 m a) electric field at P due to b isb/(2o), electric field at Pdue to t is-t/(2o) so net electric field at P is E = (b -t)/(2o) = -5.36*105N/C negative means -z direction b) since q is negative, it will hit the positive, or the topplate. Force on q is F = qE work done by the field is -F*(z - zo) = 0.402 J thatequals to kinetic energy when hit. mv2/2 = 0.402 v = 40.1 m/s

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