TS EAMCET · Physics · Motion In One Dimension

If $ε_{0}$ and $μ_{0},$ represent the permittivity and permeability of free space respectively, then the dimension of the product $ε_{0} μ_{0}$ is,

A $M^{0} L^{- 2} T^{2}$
B $M^{0} L^{2} T^{- 2}$
C $M^{0} L T^{- 1}$
D $M^{0} L^{- 1} T$

Verified Solution

Answer & Solution

Correct Answer

(A) $M^{0} L^{- 2} T^{2}$

Step-by-step Solution

Detailed explanation

From Maxwell's relation from electromagnetic wave, speed of light is given by, c=1μ0ε0 From Dimensional homogeneity, c=1μ0ε012 ⇒LT-1=1μ0ε012 ⇒1μ0ε0=LT-12 ⇒μ0ε0=LT-1-2 ⇒μ0ε0=L-2T2

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If ε0 and μ0, represent the permittivity and permeability of free space respectively, then the dimension of the product ε0 μ0 is,

Step-by-step Solution

If $ε_{0}$ and $μ_{0},$ represent the permittivity and permeability of free space respectively, then the dimension of the product $ε_{0} μ_{0}$ is,