Select the dimensional formula of (B2/2 μ 0) . Here B is the magnetic field and μ 0 is the permeability of the free space.

Question

Select the dimensional formula of (B2/2 μ 0) . Here B is the magnetic field and μ 0 is the permeability of the free space. (A) [M1 L1 T2] (B) [M- 1 L1 T2] (C) [M- 1 L- 1 T- 2] (D) [M1 L- 1 T- 2]

Tardigrade Admin · Accepted Answer

(B2/2 μ 0)=Energy density=(E n e r g y/V o l u m e) ⇒ ([ML2 T- 2]/[L3])=[ML- 1 T- 2]

Q. Select the dimensional formula of $\frac{B ^{2}}{2 μ _{0}}$ . Here $B$ is the magnetic field and $μ_{0}$ is the permeability of the free space.

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

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

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

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

$\frac{B ^{2}}{2 μ _{0}} = E n er g y d e n s i t y = \frac{E n er g y}{V o l u m e}$
$\Rightarrow \frac{[ M L ^{2} T ^{- 2} ]}{[ L ^{3} ]} = [M L^{- 1} T^{- 2}]$

Q. Select the dimensional formula of 2μ0​B2​ . Here B is the magnetic field and μ0​ is the permeability of the free space.

[M1L1T2]

[M−1L1T2]

[M−1L−1T−2]

[M1L−1T−2]

2μ0​B2​=Energydensity=VolumeEnergy​ ⇒[L3][ML2T−2]​=[ML−1T−2]

Q. Select the dimensional formula of $\frac{B ^{2}}{2 μ _{0}}$ . Here $B$ is the magnetic field and $μ_{0}$ is the permeability of the free space.

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

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

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

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

$\frac{B ^{2}}{2 μ _{0}} = E n er g y d e n s i t y = \frac{E n er g y}{V o l u m e}$
$\Rightarrow \frac{[ M L ^{2} T ^{- 2} ]}{[ L ^{3} ]} = [M L^{- 1} T^{- 2}]$