QJEEM13Ph89c4: JEE Main 2013 Physics - Class 11 JEEM13Ph89c4 Solution: Let [ ε 0 ] denote the dimensional formula of the permittivity…

Question

Verified Solution • 2025–26 Session moderate

Let [

ε_{0}

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

Accepted Answer

From Coulomb's law we know,

F = \frac{1}{4 π \in_{0}} \frac{q_{1} q_{2}}{r^{2}}

∴

\in_{0} = \frac{1}{4 π} \frac{q_{1} q_{2}}{F r^{2}}

Hence,

[\in_{0}] = \frac{[A T] [A T]}{[M L T^{- 2}] [L^{2}]}

=

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

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