Let [ ε 0 ] denote the dimensional formula of the permittivity of the vacuum and [ μ 0 ] that of the permeability of the vacuum. If M = mass, L = length, T = time and I = electric current. (JEE 19

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Let [ ε 0 ​ ] denote the dimensional formula of the permittivity of the vacuum and [ μ 0 ​ ] that of the permeability of the vacuum. If M = mass, L = length, T = time and I = electric current. (JEE 1998)

TestHub · Accepted Answer

From F = 4 π ε 0 ​ 1 ​ r 2 q 1 ​ q 2 ​ ​ : [ ε 0 ​ ] = [ M L T − 2 ] [ L 2 ] ([ I T ] ) 2 ​ = [ M − 1 L − 3 T 4 I 2 ] . From c = ε 0 ​ μ 0 ​ ​ 1 ​ : [ μ 0 ​ ] = [ ε 0 ​ ] [ c 2 ] 1 ​ = [ M − 1 L − 3 T 4 I 2 ] ( [ L T − 1 ] ) 2 1 ​ = [ M L T − 2 I − 2 ] .

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