Q. The dimensions of $\frac{1}{2}\varepsilon_{o}E^{2}\ (\varepsilon_{o}:$permittivity of free space; $E$: electric field) is
A) [MLT]
B) $\left\lbrack ML^{2}T^{- 2} \right\rbrack$
C) $\left\lbrack ML^{- 1}T^{- 2} \right\rbrack$
D) $\left\lbrack ML^{2}T^{- 1} \right\rbrack$
Explanation
(c) $\therefore\ \left\lbrack \varepsilon_{o} \right\rbrack = \lbrack M^{- 1}L^{- 3}T^{4}A^{2}\rbrack$ and $\lbrack E\rbrack = \ \lbrack MLT\ ^{- 3}A^{- 1}\rbrack$
$\therefore\ \left\lbrack \frac{1}{2}\varepsilon_{o}E^{2} \right\rbrack = \left\lbrack M^{- 1}L^{- 3}T^{4}A^{2} \right\rbrack \times \left\lbrack MLT^{- 3}A^{- 1} \right\rbrack^{2}$
$= \lbrack ML^{- 1}T^{- 2}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.