The dimension of (1/2)ε 0 E2, where ε 0 is permittivity of free space and E is electric field, is

Question

The dimension of (1/2)ε 0 E2, where ε 0 is permittivity of free space and E is electric field, is (A) ML2T-2 (B) ML-1T-2 (C) ML2T-1 (D) MLT-1

Tardigrade Admin · Accepted Answer

Energy density of an electric field E is uE=(1/2)ε 0 E2 where ε 0 is permittivity of free space uE=( textEnergy/ textVolume) =(ML2T-2/L3) =ML-1T-2 Hence, the dimension of (1/2)ε 0 E2 is ML-1T-2

Q. The dimension of $\frac{1}{2} ε_{0} E^{2}$ , where $ε_{0}$ is permittivity of free space and $E$ is electric field, is

$M L^{2} T^{- 2}$

$M L^{- 1} T^{- 2}$

$M L^{2} T^{- 1}$

$M L T^{- 1}$

Energy density of an electric field $E$ is
$u_{E} = \frac{1}{2} ε_{0} E^{2}$
where $ε_{0}$ is permittivity of free space
$u_{E} = \frac{Energy}{Volume}$
$= \frac{M L ^{2} T ^{- 2}}{L ^{3}}$
$= M L^{- 1} T^{- 2}$
Hence, the dimension of $\frac{1}{2} ε_{0} E^{2}$ is $M L^{- 1} T^{- 2}$

Q. The dimension of 21​ε0​E2, where ε0​ is permittivity of free space and E is electric field, is

ML2T−2

ML−1T−2

ML2T−1

MLT−1