Physics Q35 – JEE-MAIN 2025

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 :

Clue 1 of 3: Fundamental Constants

Recall the relationship between the permeability of free space ( $μ_{0}$ ), permittivity of free space ( $ϵ_{0}$ ), and a fundamental physical constant.

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Ninja Strategy•Recognize the Speed of Light

The expression $\frac{1}{μ_{0} ϵ_{0}}$ is equal to $c^{2}$ , where $c$ is the speed of light. The dimension of speed is length per time ( $L / T$ ), so the dimension of $c^{2}$ must be $(L / T)^{2} = L^{2} / T^{2}$ .

🧠 Full Solution Path

Step 1: Relate the expression to a known physical constant✦ Active

The speed of light in free space, $c$ , is given by the formula:

c = \frac{1}{\sqrt{μ_{0} ϵ_{0}}}

Squaring both sides, we get:

c^{2} = \frac{1}{μ_{0} ϵ_{0}}

Step 2: Determine the dimensions of the related constant○ Expand

The dimension of speed ( $c$ ) is $[L T^{- 1}]$ , where $L$ represents length and $T$ represents time.

Step 3: Calculate the dimension of the expression○ Expand

Since $\frac{1}{μ_{0} ϵ_{0}} = c^{2}$ , its dimension will be the square of the dimension of speed:

[c^{2}] = [L T^{- 1}]^{2} = [L^{2} T^{- 2}]

Therefore, the dimension of $(\frac{1}{μ_{0} ϵ_{0}})$ is $L^{2} / T^{2}$ .

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Physics Question 35 – JEE-MAIN 2025

Clue 1 of 3: Fundamental Constants

🧠 Full Solution Path