Bubble diagram with electrostatic energy

The bubble diagram introduced in the chapter on energy extends naturally to electrostatics: just add a bubble for the electrostatic potential energy $E_{\text{pot,el}}$. The system of two charges is represented with this central bubble, connected to the two kinetic energies of the particles on either side.

Bubble diagram for two charges: $E_{\text{pot,el}}$ in the centre, the two kinetic energies on either side. If the system is isolated, the total energy $E_{\text{tot}}$ is conserved: each top row is the initial state, each bottom row the final state.

The reading is the usual one: each bubble contains the initial value (top) and final value (bottom) of that type of energy; the arrows show internal transfers. Since the system is isolated, no arrow crosses the dashed boundary and the sum of the contents stays constant.

The most instructive case is that of two charges that attract each other ($q_1 q_2 < 0$). The potential energy is negative and, as the charges approach, it becomes more negative: its absolute value grows. That “released” energy does not vanish, but flows into the two side kinetic bubbles, which fill up: the particles accelerate. This is exactly what happens in problems with two charges released from rest, where the drop in $E_{\text{pot,el}}$ fixes the overall final kinetic energy.

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Topics: Electrostatics Concepts: Electrostatic potential energy Skills: Bubble energy balance Methods: Bubble diagram of energy exchange

Related exercises: Problem — Collision between charges with friction · Problem — Two charges released from rest · Problem — The two gunslingers