If and are the permeability and permittivity of free space, respectively. then the dimension of is : [2025]

Question

If $μ_{0}$ and $ε_{0}$ are the permeability and permittivity of free space, respectively. then the dimension of $(\frac{1}{μ_{0} ε_{0}})$ is : [2025]

Smart Achievers · Accepted Answer

(2)

$C = \frac{1}{\sqrt{μ_{0} ε_{0}}}$

$μ_{0} ε_{0} \equiv \frac{1}{C^{2}} \equiv [L^{- 2} T^{2}]$

$∴ [\frac{1}{μ_{0} ε_{0}}] = \frac{L^{2}}{T^{2}}$

Solution

Q.
If $μ_{0}$ and $ε_{0}$ are the permeability and permittivity of free space, respectively. then the dimension of $(\frac{1}{μ_{0} ε_{0}})$ is : [2025]

1 $L / T^{2}$

2 $L^{2} / T^{2}$

3 $T^{2} / L$

4 $T^{2} / L^{2}$

Ans.
(2)

$C = \frac{1}{\sqrt{μ_{0} ε_{0}}}$

$μ_{0} ε_{0} \equiv \frac{1}{C^{2}} \equiv [L^{- 2} T^{2}]$

$∴ [\frac{1}{μ_{0} ε_{0}}] = \frac{L^{2}}{T^{2}}$

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Solution

Q. If μ0 and ε0 are the permeability and permittivity of free space, respectively. then the dimension of (1μ0ε0) is : [2025]

1 L/T2

2 L2/T2

3 T2/L

4 T2/L2

Ans. (2) C=1μ0ε0 μ0ε0≡1C2≡[L–2T2] ∴ [1μ0ε0]=L2T2