The dimensional formula of (1/2) μ0 H2 (μ= permeability of free space and H= magnetic field intensity) is

Question

The dimensional formula of (1/2) μ0 H2 (μ= permeability of free space and H= magnetic field intensity) is (A) [ MLT -1] (B) [ ML 2 T -2] (C) [ ML -1 T -2] (D) [ ML 2 T -1]

Tardigrade Admin · Accepted Answer

[μ0]=[ MLT -2 A -2] and [H]=[ AL -1] ∴ [(1/2) μ0 H2]=[ MLT -2 A -2][ AL -1]2=[ ML -1 T -2]

Q. The dimensional formula of $\frac{1}{2} μ_{0} H^{2}$ $(μ =$ permeability of free space and $H =$ magnetic field intensity) is

$[M L T^{- 1}]$

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

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

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

$[μ_{0}] = [M L T^{- 2} A^{- 2}]$ and $[H] = [A L^{- 1}]$
$∴ [\frac{1}{2} μ_{0} H^{2}] = [M L T^{- 2} A^{- 2}] [A L^{- 1}]^{2} = [M L^{- 1} T^{- 2}]$

Q. The dimensional formula of 21​μ0​H2 (μ= permeability of free space and H= magnetic field intensity) is

[MLT−1]

[ML2T−2]

[ML−1T−2]

[ML2T−1]