Units & Dimensions

JEE Main level, single correct, medium

73 of 149

Question 73 of 149

Dimension of 1μ0ϵ0\dfrac{1}{{\mu }_{0}{\epsilon }_{0}} should be equal to

Show answer and solution

Answer: (C) L2T−2{L}^{2}{T}^{-2}

The speed of light can be written as
c=1μ0ϵ0...(1)c=\dfrac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}}...\left(1\right)
Rearrange equation (1) to obtain the required quantity.
1μ0ϵ0=c2...(2)\dfrac{1}{{\mu }_{0}{\epsilon }_{0}}={c}^{2}...\left(2\right)
Use the method of dimensional analysis to obtain the dimension of the required quantity.
[1μ0ϵ0]=[LT−1]2=L2T−2\begin{matrix}\left[\dfrac{1}{{\mu }_{0}{\epsilon }_{0}}\right] & = & {\left[L{T}^{-1}\right]}^{2} \\ & = & {L}^{2}{T}^{-2}\end{matrix}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Units & Dimensions (Dimensions), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.