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Units and Measurements question

2003 · Shift 0 · Q170
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Units and Measurements question

2003 · Shift 0 · Q170

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
Dimensions of 1μ0ε0{1 \over {{\mu _0}{\varepsilon _0}}}μ0​ε0​1​, where symbols have their usual meaning, are
  1. A
    [ L-1T ]
  2. B
    [ L-2T2 ]
  3. C
    [ L2T-2 ]
  4. D
    [ LT-1 ]
View written solutionFree

Correct answer: C

  1. We use the standard relation between permeability and permittivity:
μ0ε0=1c2\mu_0 \varepsilon_0 = \frac{1}{c^2}μ0​ε0​=c21​

where ccc is the speed of light.

  1. Therefore,
1μ0ε0=c2\frac{1}{\mu_0 \varepsilon_0} = c^2μ0​ε0​1​=c2
  1. Now, the dimensions of speed ccc are
[c]=[LT−1][c] = [LT^{-1}][c]=[LT−1]

So,

[c2]=[L2T−2][c^2] = [L^2T^{-2}][c2]=[L2T−2]
  1. Hence,
[1μ0ε0]=[L2T−2]\left[\frac{1}{\mu_0 \varepsilon_0}\right] = [L^2T^{-2}][μ0​ε0​1​]=[L2T−2]
  1. Compare with the options:
  • A: [L−1T][L^{-1}T][L−1T]
  • B: [L−2T2][L^{-2}T^2][L−2T2]
  • C: [L2T−2][L^2T^{-2}][L2T−2]
  • D: [LT−1][LT^{-1}][LT−1]

So the correct option is C.

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