(Solved): Two concentric conducting spheres have radii of \( a \) and \( b \), respectively, and carry charg ...

Two concentric conducting spheres have radii of \( a \) and \( b \), respectively, and carry charge \( -Q \) and \( +Q \), respectively. A portion of the space between the spheres is filled with a dielectric material of dielectric constant \( \varepsilon \), as shown in the figure below. a) Find the electric field everywhere between the spheres. (10 pts) b) Find the surface-charge distribution on the inner sphere. (10 pts) c) Find the polarization-charge density on the surface of the dielectric at \( r=a \). (10 pts)