> There is no such thing as "proof" of Maxwell's equations.
Is there proof of any "physics"?
Physics is the science that studies "physical models", which are just that, "models". Whether a model is useful (or not), or how accurate a model is, is determined by using the model to make a prediction, and then doing an experiment to check how bad the prediction is. Measuring a prediction is hard, and typically requires repeating the same experiment many many times, which at best produces a probability density distribution of the prediction the model should produce.
This process is called "model validation", but it does not prove the model correct. For example, we can validate Newton's laws to predict the weight of many objects on earth relatively accurately. But this does not mean that Newton's laws are correct, that they would produce correct outcomes if you were moving at the speed of light, etc.
When people talk about "proving physical models correct", I honestly have no idea what is it that they want, or how do they expect that this is done. If God was real and would answer to us, I guess we could ask God if a particular model is correct. But that's the only way I can think of to deliver one of these "proofs".
> Physics is the science that studies "physical models"
This is a completely wrong thing to say. Physics studies (some aspects of) Nature by creating models and testing their predictions.
(You as a student might well be studying "physical models", but it would be a funny thing to say that for example "biology is a science where the teacher is yelling at students while trying to attract their attention to some nasty-looking posters.")
Is there proof of any "physics"?
Physics is the science that studies "physical models", which are just that, "models". Whether a model is useful (or not), or how accurate a model is, is determined by using the model to make a prediction, and then doing an experiment to check how bad the prediction is. Measuring a prediction is hard, and typically requires repeating the same experiment many many times, which at best produces a probability density distribution of the prediction the model should produce.
This process is called "model validation", but it does not prove the model correct. For example, we can validate Newton's laws to predict the weight of many objects on earth relatively accurately. But this does not mean that Newton's laws are correct, that they would produce correct outcomes if you were moving at the speed of light, etc.
When people talk about "proving physical models correct", I honestly have no idea what is it that they want, or how do they expect that this is done. If God was real and would answer to us, I guess we could ask God if a particular model is correct. But that's the only way I can think of to deliver one of these "proofs".