captain said:
Your teacher is right on this one. The A-potential is introduced in the EM formalism to write the theory in a symmetrical way. It makes the step towards field theory more logic in the sense that the A field plays the role of the EM gauge field. Also, this potential is used to impose gauge-conditions to set the remaining degree of freedom that arises due to the definition of the A-field.Pythagorean said:
(hint : look at the definition of the scalar potential)Pythagorean said:
The vector potential in physics is a mathematical construct used to describe the behavior of vector fields in three-dimensional space. It is commonly used in electromagnetism to represent the magnetic field in terms of a scalar potential and a vector potential.
The electric and magnetic fields can be derived from the vector potential using the equations E = -∂A/∂t and B = ∇ x A. This relationship is known as the vector potential gauge invariance and allows for a more elegant and concise representation of electromagnetic phenomena.
The vector potential is physically significant because it represents the underlying structure of electromagnetic fields. It helps us understand the behavior of these fields and can be used to make predictions and calculations in various applications, such as in electric motors and generators.
The proof of this equation involves using Maxwell's equations and the vector potential gauge invariance to show that the electric field can be expressed as the negative gradient of the scalar potential (φ) and the time derivative of the vector potential (A).
The vector potential cannot be directly measured as it is a mathematical construct. However, it can be calculated or inferred from measurements of the electric and magnetic fields using the equations mentioned above. It is also important to note that the vector potential is only defined up to a constant, so its absolute value cannot be measured.