In S I units, the dimensions of ϵ 0 μ 0 is:

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

In

S I

units, the dimensions of

\sqrt{\frac{ϵ_{0}}{μ_{0}}}

is:

PhysicsUnits and DimensionsJEE MainJEE Main 2019 (08 Apr Shift 1)

Options:

A $A T^{2} M^{- 1} L^{- 1}$
B $A^{2} T^{3} M^{- 1} L^{- 2}$
C $A^{- 1} T M L^{3}$
D $A T^{- 3} M L^{3 / 2}$

Solution:

1471 Upvotes Verified Answer

The correct answer is:

A^{2} T^{3} M^{- 1} L^{- 2}

As we know,

c = \frac{1}{\sqrt{μ_{0} ε_{0}}}

∴ \sqrt{\frac{ε_{0}}{μ_{0}}} = \sqrt{\frac{ε_{0}^{2}}{μ_{0} ε_{0}}} = ε_{0} c

∴ [\sqrt{\frac{ε_{0}}{μ_{0}}}] =

[ε_{0}] [c] = [M^{- 1} L^{- 3} T^{4} A^{2}] [L T^{- 1}]

= [M^{- 1} L^{- 2} T^{3} A^{2}]

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play