The dimension of ( e 2/4 π ε0 hc ), where e , ε0, h and c are electric charge, electric permittivity, Planck's constant and velocity of light in vacuum respectively

Question

The dimension of ( e 2/4 π ε0 hc ), where e , ε0, h and c are electric charge, electric permittivity, Planck's constant and velocity of light in vacuum respectively (A) [ M 0 L 0 T 0] (B) [ ML 0 T 0] (C) [ M 0 LT 0] (D) [ M 0 L 0 T ]

Tardigrade Admin · Accepted Answer

We know that, [ e ]=[ AT ], [ε0]=[ M -1 L -3 T 4 A 2], ∴ [( e 2/4 π ε0 hc )] =[( A 2 T 2/ M -1 L -3 T 4 A 2 × ML 2 T -1 × LT -1)] =[ M 0 L 0 T 0]

Q. The dimension of $\frac{e ^{2}}{4 π ε _{0} h c},$ where $e, ε_{0}, h$ and $c$ are electric charge, electric permittivity, Planck's constant and velocity of light in vacuum respectively

$[M^{0} L^{0} T^{0}]$

$[M L^{0} T^{0}]$

$[M^{0} L T^{0}]$

$[M^{0} L^{0} T]$

We know that, $[e] = [A T]$ ,
$[ε_{0}] = [M^{- 1} L^{- 3} T^{4} A^{2}]$ ,
$∴ [\frac{e ^{2}}{4 π ε _{0} h c}]$
$= [\frac{A ^{2} T ^{2}}{M ^{- 1} L ^{- 3} T ^{4} A ^{2} \times M L ^{2} T ^{- 1} \times L T ^{- 1}}]$
$= [M^{0} L^{0} T^{0}]$

Q. The dimension of 4πε0​hce2​, where e,ε0​,h and c are electric charge, electric permittivity, Planck's constant and velocity of light in vacuum respectively

[M0L0T0]

[ML0T0]

[M0LT0]

[M0L0T]