PHYS 102 | E-Field in a 3D Dielectric 1 - Volume Bound Charge (really!)

We start with a 3D structure: a dielectric sphere with a point charge at the center, which leads to the concept of volume bound charge.
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[@usersn300]

Very strange, that only few viewers with good quality content.

[@Prof-Hafner]

Not too many people on CZcams want to know about the bound charge in a dielectric. 😂

[@vegbetle]

good video

[@terenzocollina8410]

Is it wrong to say that bound density charge is equal to zero with a linear dielectric since divergence of D is zero?

[@Prof-Hafner]

I don't think so. Everything I present is about linear dielectrics. You get bound charge when you have a non-uniform field.

[@terenzocollina8410]

@@Prof-Hafner
I also thought that with a non-uniform field there were bound density polarization charges, but suppose the dielectric is linear(P is linearly proportional with E) and suppose it is also isotropic and homogeneus (so it is independent of witch direction we take and the constants vacuum permittivity and electric susceptibility ε_o and χ are constant in all of the dielectric) .
Now we know P = (ε_o)χE and D = (ε_o)E+P
So we have P = χ/(χ+1)D = ((k-1)/k)D With k as the relative dielectric constant
Dielectric is homogeneous so if we calculate the divergence of P we can write Div(P)=((k-1)/k)Div(D)
And we are in a dielectric so there are no free charges so Div(D)=0 and so Div(P)=0 from the previous relationship, but we also know that the divergence of P is related to the bound density charge in a dielectric with Div(P)=-ρ , but Div(P)=0 so ρ is zero (and from the slides of my professor he also adds “this happens also if E and P are not uniform inside the dielectric”).