Question

$\frac{E^{2}}{\mu_{0}}$has the dimensions (E = electric field, µ₀ = permeability of free space) –

• A. $\lbrack M^{2}L^{3}T^{\text{-2}}A^{2}\rbrack$
• B. $\lbrack\text{ML}\text{T}^{\text{-4}}\rbrack$
• C. $\lbrack\text{M}\text{L}^{3}T^{\text{-2}}\rbrack$
• D. $\lbrack M^{\text{-1}}L^{2}\text{T}\text{A}^{\text{-2}}\rbrack$

Answer 1

Answer: (B)

$\lbrack\text{ML}\text{T}^{\text{-4}}\rbrack$

Answer 2

$\left\lbrack \frac{E^{2}}{\mu_{0}} \right\rbrack = \left\lbrack \frac{\varepsilon_{0}E^{2}}{\varepsilon_{0}\mu_{0}} \right\rbrack = \left\lbrack \frac{energy/volume}{(1/speedoflight)^{2}} \right\rbrack$

$= \left\lbrack \frac{energy(speed)^{2}}{volume} \right\rbrack$

$= \left\lbrack \frac{ML^{2}T^{- 2}L^{2}T^{- 2}}{L^{3}} \right\rbrack = \ \lbrack\text{ML}\text{T}^{\text{-4}}\rbrack$