Yes, you can think of their expression as coming from ΔV=-∫E dl if you express E in terms of D. Use Gauss' law for D to obtain an explicit expression for D in terms of the free charge Q on the inner conductor.Cocoleia said:
An electric field is a physical quantity that describes the influence of electric charges on each other. It is a vector field, meaning it has both magnitude and direction, and it is created by the presence of electric charges.
Electric field strength is measured in units of volts per meter (V/m). It can be measured using a device called an electric field meter, which detects the force exerted on a charged object placed in the field.
Surface charge density is a measure of the amount of electric charge per unit area on the surface of a conductor. It is represented by the symbol σ and is measured in units of coulombs per square meter (C/m^2).
Surface charge density has a direct relationship with the electric field. The higher the surface charge density, the stronger the electric field will be at that point. This is because the electric field is created by the presence of electric charges, and a higher surface charge density means there are more charges in a given area.
Electric field and surface charge density are related but different concepts. Electric field is a physical quantity that describes the influence of electric charges on each other, while surface charge density is a measure of the amount of electric charge per unit area on the surface of a conductor. In other words, the electric field is the cause of the surface charge density, and the surface charge density is the effect of the electric field.