# Do field and potential energy always come together?

1. Is energy directly due to a field always potential energy?
2. Is potential energy always due to a field?

a field is a physical quantity that has a value for each point in spacetime.

potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system.

Thanks!

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Quite generally, I think that you should appreciate that there may exist many forms of energy. The energy is the most general formula for a conserved quantity that typically contains many terms. These terms may depend on the positions of particles, velocities of particles, values of the fields, and the rate of change of fields as functions of spatial directions as well as time. The term "potential energy" is usually reserved for terms in energy that don't depend on derivatives. However, the potential energy between two electric charges, for example, boils down to the $E^2/2$ term in the energy density of the electric field and here, $E$ contains $\partial A/\partial t$, so it's a "kinetic term for the field $\vec A$", anyway. In general, one must be careful about the classification of terms in the energy to potential and others (e.g. kinetic). It's always more accurate to mathematically express what particular term or what class of terms we are talking about.