Question

Which of the following physical quantities have the same dimensions?

• A. Electric displacement $(\vec{D})$ and surface charge density
• B. Displacement current and electric field
• C. Current density and surface charge density
• D. Electric potential and energy

Answer 1

The Correct Option is A

Electric displacement \(\vec D=\epsilon_0\vec E\)
\([\vec D]=[\epsilon_0][\vec E]\)
\([M^{-1}L^{-3}T^4A^2][M^1L^1A^{-1}T^{-3}]\)
\([\vec D]=[L^{-2}T^1A^1]\)
[D]=[\(\sigma\)]
Surface change density = \(|\frac{Q}{A}|\)
\([\sigma]=[ATL^{-2}]\)
So, Electric displacement and Surface charge density have the same units.

Therefore the correct option is (A): Electric displacement (\(\vec D\)) and surface charge density.