Let [ε₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then

[ε₀] = [M^-1L^-3T²A]

[ε₀] = [M^-1L^-3T⁴A²]

[ε₀] =[M^-2L²T^-1A^-2]

[ε₀] = [M^-1L²T^-1A²]

Solution

[ε₀] = [M^-1L^-3T⁴A²]

From Coulomb's Law, F
$straight F space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight R squared end fraction straight epsilon subscript straight o space equals space fraction numerator straight q subscript 1 straight q subscript 2 over denominator 4 πFR squared end fraction$
On Substituting the units, we get

$straight epsilon subscript straight o space equals space fraction numerator straight C squared over denominator straight N minus straight m end fraction space equals space fraction numerator left square bracket AT right square bracket squared over denominator left square bracket MLT to the power of negative 2 end exponent right square bracket left square bracket straight L squared right square bracket end fraction space left parenthesis 4 straight pi space is space dimensionless right parenthesis space equals space left square bracket straight M to the power of negative 1 end exponent straight L to the power of negative 3 end exponent straight T to the power of 4 straight A squared right square bracket$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

Let [ε₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then

[ε₀] = [M^-1L^-3T²A]

[ε₀] = [M^-1L^-3T⁴A²]

[ε₀] =[M^-2L²T^-1A^-2]

[ε₀] = [M^-1L²T^-1A²]

Some More Questions From Units and Measurement Chapter

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

How many fundamental quantities are there in Physics?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Units And Measurement

Let [ε0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then [ε0] = [M-1L-3T2A] [ε0] = [M-1L-3T4A2] [ε0] =[M-2L2T-1A-2] [ε0] = [M-1L2T-1A2]

Some More Questions From Units and Measurement Chapter

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

How many fundamental quantities are there in Physics?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Let [ε₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then

[ε₀] = [M^-1L^-3T²A]

[ε₀] = [M^-1L^-3T⁴A²]

[ε₀] =[M^-2L²T^-1A^-2]

[ε₀] = [M^-1L²T^-1A²]