Centre of Curvature: Turning Point or Centre?

[Masafi]

A proton is deflected by a magnetic field, and curves away.

It states that just before it curves, the force acts towards the centre of curvature. Is this the point where it turns, i.e. the turning point of the parabola, or the centre being like the centre of a circle?

 

[tiny-tim]

Hi songoku!

It states that just before it curves, the force acts towards the centre of curvature. Is this the point where it turns, i.e. the turning point of the parabola, or the centre being like the centre of a circle?

ah, this is geometry …

the centre of curvature of any curve (at a particular point) is the centre of the circle that "best fits" the curve at that point …

imagine blowing up a balloon that sits on the curve: eventually it will become so big that it can't still touch the curve at that point: just before that happens, the balloon has the same radius of curvature as the curve, and the centre of curvature is the centre of the balloon.

(so "towards the centre of curvature" simply means perpendicular to the tangent, on the concave side of the curve )​