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In electromagnetism, we can re-write the electric field in terms of the electric scalar potential, and the magnetic vector potential. That is:

$$E = -\nabla\phi - \frac{\partial A}{\partial t}$$, where A$$A$$ is such that $$B = \nabla \times A$$.

I have an intuitive understanding of $$\phi$$ as the electric potential, as I am familiar with the formula $$F = -\nabla V$$, where $$V$$ is the potential energy. Therefore since $$E = F/q$$, it is easy to see how $$\phi$$ can be interpreted as the electric potential, in the electrostatic case.

I also know that $$F = \frac{dp}{dt}$$, where $$p$$ is momentum, and thus this leads me to believe that $$A$$ should be somehow connected to momentum, maybe like a "potential momentum". Is there such an intuitveintuitive way to understand what $$A$$ is physically?

In electromagnetism, we can re-write the electric field in terms of the electric potential, and the magnetic vector potential. That is:

$$E = -\nabla\phi - \frac{\partial A}{\partial t}$$, where A is such that $$B = \nabla \times A$$.

I have an intuitive understanding of $$\phi$$ as the electric potential, as I am familiar with the formula $$F = -\nabla V$$, where $$V$$ is the potential energy. Therefore since $$E = F/q$$, it is easy to see how $$\phi$$ can be interpreted as the electric potential, in the electrostatic case.

I also know that $$F = \frac{dp}{dt}$$, where $$p$$ is momentum, and thus this leads me to believe that $$A$$ should be somehow connected to momentum, maybe like a "potential momentum". Is there such an intuitve way to understand what $$A$$ is physically?

In electromagnetism, we can re-write the electric field in terms of the electric scalar potential, and the magnetic vector potential. That is:

$$E = -\nabla\phi - \frac{\partial A}{\partial t}$$, where $$A$$ is such that $$B = \nabla \times A$$.

I have an intuitive understanding of $$\phi$$ as the electric potential, as I am familiar with the formula $$F = -\nabla V$$, where $$V$$ is the potential energy. Therefore since $$E = F/q$$, it is easy to see how $$\phi$$ can be interpreted as the electric potential, in the electrostatic case.

I also know that $$F = \frac{dp}{dt}$$, where $$p$$ is momentum, and thus this leads me to believe that $$A$$ should be somehow connected to momentum, maybe like a "potential momentum". Is there such an intuitive way to understand what $$A$$ is physically?

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# How to interpret the magnetic vector potential?

In electromagnetism, we can re-write the electric field in terms of the electric potential, and the magnetic vector potential. That is:

$$E = -\nabla\phi - \frac{\partial A}{\partial t}$$, where A is such that $$B = \nabla \times A$$.

I have an intuitive understanding of $$\phi$$ as the electric potential, as I am familiar with the formula $$F = -\nabla V$$, where $$V$$ is the potential energy. Therefore since $$E = F/q$$, it is easy to see how $$\phi$$ can be interpreted as the electric potential, in the electrostatic case.

I also know that $$F = \frac{dp}{dt}$$, where $$p$$ is momentum, and thus this leads me to believe that $$A$$ should be somehow connected to momentum, maybe like a "potential momentum". Is there such an intuitve way to understand what $$A$$ is physically?