The dimensional formula for permittivity of free space ε 0 in the equation F = 1 4 π ε 0 q 1 q 2 r 2 , where symbols have their usual meaning, is

As, F = 1 4 π ε 0 q 1 q 2 r 2 ⇒ ε 0 = q 1 q 2 4 π F r 2 = T A 2 L 2 M L T - 2 = M - 1 L - 3 T 4 A 2

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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

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The dimensional formula for permittivity of free space $(ε_{0})$ in the equation $F = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r^{2}}$ , where symbols have their usual meaning, is

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Solution:

As, $F = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r^{2}}$

$\Rightarrow ε_{0} = \frac{q_{1} q_{2}}{4 π F r^{2}}$

$= \frac{{[T A]}^{2}}{[L^{2}] [M L T^{- 2}]}$

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

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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