Three charged rods all with the same magnitude charge, one with net charge + Q_o

Question

Three charged rods all with the same magnitude charge, one with net charge + Q_o and two with Q_o are held in place as shown in the top view diagram below. A small test charge + q_o travels from point A to point D along the path described. First the test charge travels along a straight line from A to B. Then it travels from B to C along the semicircle as shown in the diagram. Finally it travels along a straight line from C to D. For each of these paths, is the net week done on the charge +q_o by the electric field positive, negative, or zero? Explain your reasoning. W_a-b +, force and direction same W_a-c Cos 90: 0 W_C-D force & direction opposite Rank from highest to lowest, the electric potentials at points A, B, C, and D. Explain, V_A > V_S > V_e > V_O as more h, less V_E Suppose a particle with charge + Q_o and mass m_o is released from rest at point A and observed to pass point B with a speed 9 m/s. If this particle were released from rest at point C, would its speed be greater than, less than, or equal to 9 m/s when it passed point D? Explain. If a different particle with charge + 16Q_o and mass m_o were released from rest at point A, what speed would it have when it passed point B? Explain.

Explanation / Answer

b)change in KE = q deltaV

m( 9^2 - va^2) /2 = q ( Va - Vb)

m( 9^2 )/ 2 = 1.05kQq/r

PE diff from C to D is 0.5kQq/r that less than Va-Vb hence
speed will be less than 9 m/s.

ii) now m v^2 /2 = q (Va - Vb) = 16 ( 1.05kQq/r )

and m( 9^2 )/ 2 = 1.05kQq/r (in above part)

m v^2 /2 = 16 m (9^2) /2

v = 36 m/s

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