$\begingroup$I'm currently in an electrostatics course; and wanting to rip my hair out.
The question says:
A sphere of radius 𝑎 is polarized such that the polarization at 𝒓 within the sphere is given by 𝑷 = 𝑘𝑟𝒓̂ , where 𝑘 is a constant and 𝒓 is the radial position vector from the centre of the sphere.
It asks:
a) Find the bound surface charge density 𝜎𝑏 and the bound volume charge density 𝜌𝑏. b) Find the electric field inside and outside the sphere
My question from all of this is what is the radial vector? I don't actually know what it means for something to be pointing radially and I haven't found much luck through web searches.
$\endgroup$22 Answers
$\begingroup$The radial direction points from the center of the sphere towards the surface. Since the sphere is radially symmetrical, any vector with its beginning at the center point of the sphere and its end point on the surface will qualify.
$\endgroup$1$\begingroup$The radial direction is somehow like what you think of "radius".
Just imagine a ball:you define the ridius of the ball as the distance from the center to the point on the surface
Connect the two points:the direction is just go alongside the line you draw,from the center,to any point on the surface
$\endgroup$
