A charge q that moves between two points A and B, and has an electric force acti

Question

A charge q that moves between two points A and B, and has an electric force acting on it ( and perhaps several other forces) has work W done on it by the electric force. The electrostatic force is conservative and so we can define a change in electric potential energy, Delta U = -W. We defined electric field using the relation F^^-> = q E^^->, and in a similar way we define electric potential commonly called voltage as
Delta V = V_B - V_A = -W/q=(Delta U)/q or equivalently q Delta V = q (V_B - V_A) = -W=Delta U

A ball has mass 3.0 µg and charge -6 nC moves from point A to point B. It has the same speed at points A and B, and the work done by the electric field during the move is -1.5 mJ.
(a) What is the change in electric potential energy of the ball? 1
(b) What is the change in voltage between points A and B? 2
(c) At which point does the ball have a higher electric potential energy?
(d) Which point has the higher voltage?
(e) Has the kinetic energy of the ball changed?

Explanation / Answer

sorry for mistakes in the previous answer. m = 3.0 µg, q = -6 nC, work done W = -1.5 mJ. (a) What is the change in electric potential energy of the ball? delta U = -W = 1.5 mJ (b) What is the change in voltage between points A and B? delta V = delta U/q = 1.5 mJ/(-6 nC) = -2.5*10^5 V (c) At which point does the ball have a higher electric potential energy? delta U = UB - UA > 0 so the ball has a higher electric potential energy at B (d) Which point has the higher voltage? delta V = VB - VA < 0 so the ball has a higher voltage at A (e) Has the kinetic energy of the ball changed? No, because the ball has same speed.

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