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Dimensional analysis and its applications

Let [_{0}] denotes the dimensional formula of the permittivity

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Solving time: 2 mins

Let $[ε_{0}]$ denotes the dimensional formula of the permittivity of vacuum. If $M =$ mass, $L =$ length, $T =$ time and $A =$ electric current, then
(a) $[ε_{0}] = [M^{- 1} L^{- 3} T^{2} A]$
(b) $[ε_{0}] = [M^{- 1} L^{- 3} T^{4} A^{2}]$
(c) $[ε_{0}] = [M^{- 2} L^{2} T^{- 1} A^{- 2}]$
(d) $[ε_{0}] = [M^{- 1} L^{2} T^{- 1} A^{2}]$

Views: 5,844 students

Updated on: Jul 9, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2013

Found 6 tutors discussing this question

Isabella Discussed

Let

[ε_{0}]

denotes the dimensional formula of the permittivity of vacuum. If

M =

mass,

L =

length,

T =

time and

A =

electric current, then
(a)

[ε_{0}] = [M^{- 1} L^{- 3} T^{2} A]

(b)

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

(c)

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

(d)

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

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Exp. (b)
Electrostatic force between two charges,

F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{R ^{2}} \Rightarrow ε_{0} = \frac{q _{1} q _{2}}{4 π F R ^{2}}

Substituting the units.
Hence,

ε_{0} = \frac{C ^{2}}{N - m ^{2}} = \frac{[ AT ] ^{2}}{[ MLT ^{- 2} ] [ L ^{2} ]}

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

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Question Text	Let $[ε_{0}]$ denotes the dimensional formula of the permittivity of vacuum. If $M =$ mass, $L =$ length, $T =$ time and $A =$ electric current, then (a) $[ε_{0}] = [M^{- 1} L^{- 3} T^{2} A]$ (b) $[ε_{0}] = [M^{- 1} L^{- 3} T^{4} A^{2}]$ (c) $[ε_{0}] = [M^{- 2} L^{2} T^{- 1} A^{- 2}]$ (d) $[ε_{0}] = [M^{- 1} L^{2} T^{- 1} A^{2}]$
Updated On	Jul 9, 2023
Topic	Units and Measurements
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	336
Avg. Video Duration	5 min

Text solutionVerified

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Let [ε0​] denotes the dimensional formula of the permittivity of vacuum. If M= mass, L= length, T= time and A= electric current, then(a) [ε0​]=[M−1 L−3 T2 A](b) [ε0​]=[M−1 L−3 T4 A2](c) [ε0​]=[M−2 L2 T−1 A−2](d) [ε0​]=[M−1 L2 T−1 A2]

Text solutionVerified

Filo tutor solutions (3)

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