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

Answer: (A)

Electric displacement $(\vec{D})$ and surface charge density

Answer 2

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**.**