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1.Units, Dimensions and Measurement
hard
Which of the following physical quantities have the same dimensions?
AElectric displacement $(\overrightarrow{ D })$ and surface charge density
BDisplacement current and electric field
CCurrent density and surface charge density
DElectric potential and energy
(JEE MAIN-2022)
Solution
Electric displacement
$\overrightarrow{ D }=\epsilon_{0} \overrightarrow{ E }$
$[ D ]=\left[\epsilon_{0} E \right]=\left[\epsilon_{0} \frac{\sigma}{\epsilon_{0}}\right]$
$[ D ]=[\sigma]$
$\rightarrow$ Surface change density $=\sigma$.
$\overrightarrow{ D }=\epsilon_{0} \overrightarrow{ E }$
$[ D ]=\left[\epsilon_{0} E \right]=\left[\epsilon_{0} \frac{\sigma}{\epsilon_{0}}\right]$
$[ D ]=[\sigma]$
$\rightarrow$ Surface change density $=\sigma$.
Standard 11
Physics
