Phase portraits (or phase diagrams) provide a powerful tool to visualize the dynamics of ODE systems.
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The electric potential energy of the charge is equal to the potential at the location of the charge, V, times the charge, q:
The potential is given by the magnitude of the electric field, E, times the distance, d:
So we have
(1)
However, the electric field is equal to the electrical force F divided by the charge q:
Therefore (1) becomes
And if we use the data of the problem, we can calculate the electrical potential energy of the charge:
The potential is given by the magnitude of the electric field, E, times the distance, d:
So we have
However, the electric field is equal to the electrical force F divided by the charge q:
Therefore (1) becomes
And if we use the data of the problem, we can calculate the electrical potential energy of the charge: