JEE MAIN - Physics (2022 - 25th July Morning Shift - No. 2)
Which of the following physical quantities have the same dimensions?
Electric displacement $$(\overrightarrow{\mathrm{D}})$$ and surface charge density
Displacement current and electric field
Current density and surface charge density
Electric potential and energy
Explicació
Electric displacement $$(\overrightarrow D ) = {\varepsilon _0}\overrightarrow E $$
$$ \Rightarrow [\overline D ] = [{\varepsilon _0}][\overline E ]$$
$$ = [{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}][{M^1}{L^1}{A^{ - 1}}{T^{ - 3}}]$$
$$[\overline D ] = [{L^{ - 2}}{T^1}{A^1}]$$
[Surface charge density] $$ = {{[Q]} \over {[A]}}$$
$$[\sigma ] = [AT{L^{ - 2}}]$$
$$ \Rightarrow \overrightarrow D $$ and $$[\sigma ]$$ have same dimensions