Why is this so (electrodynamics, coil, charge)?
I think it's about a magnetic field through a coil with a uniform current flow, with radius R. My question is, why do we have R and r? One of them is the actual radius, the other… I have no idea. Why? Is there a formula for r less than or equal to the radius and one for a radius greater than the radius? I mean, r can't mean how wide the cable is, because that's already R. But then what?
Or is r the position vector of the point you want to calculate? In other words, whether the point is still within the radius or not? How is it different outside the radius?
The same thing happened with a homogeneously charged sphere. There was something similar, the one in the picture below. And as far as I know, it was just an imaginary sphere used to calculate the electrical flux. How can anything outside the imaginary sphere be different if it's only imaginary?
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The Ampère Law describes the relationship between current and magnetic field.
It says that the magnetic flux along a closed curve is proportional to the current flow through the curve:
The curve becomes easier to integrate into the circle with radius r and with center on the center of the conductor. Thus, the magnetic field strength remains constant along the circle.
Circle larger/outside the head(r>R) closes the circle all the current
Curve integral along a closed curve:
Surface integral:
the current is only partially enclosed by the circuit:
Circle smaller/within the conductor(r
I produces the magnetic field along the closed curve.
Curve inside and outside the conductor: