In terms of potential difference `C`, electric current`I` , permittivity `epsilon_(0)`, permeability `mu_(0)` and speed of light `c`, the dimensionally correct equation `(s)` is `(are)`A. `mu_0 I^2 = epsilon_0 V^2`B. `epsilon_0 I = mu_0 V`C. `I = epsilon_0 cV`D. `mu_0 cI = epsilon_0V`

In terms of potential difference `C`, electric current`I` , permittivi

1.	In terms of potential difference `C`, electric current`I` , permittivity `epsilon_(0)`, permeability `mu_(0)` and speed of light `c`, the dimensionally correct equation `(s)` is `(are)`A. `mu_0 I^2 = epsilon_0 V^2`B. `epsilon_0 I = mu_0 V`C. `I = epsilon_0 cV`D. `mu_0 cI = epsilon_0V`
Answer» Correct Answer - (a,c) Here, Dimnsional formula for `(i) V =ML^2 T^(-3) A^(-1)` `(ii) I= [A^1]` (iii) `c= [LT^(-1)]` (iv)`epsilon_0 = [M^(-1) L^(-3) T^4 A^2]` (v) `mu_0 =[M^1 L^1 T^(-2) A^(-2)]` (a) `mu_o I^2 =epsilon_0 V^2` `MLT^(-2) A^(-2)xxA^2 = M^(-1) L^(-3) T^4 A^2xx(ML^2 T^(-3) A^(-1))^2` `MLT^(-2) = MLT^(-2)` Hence option (a) is correct. (b) `epsilon_0I =mu_0V` `M^(-1)L^(-3) T^2 A^2xxA = M^1 L^1 T^(-2) A^(-2)xxML^2 T^(-3)A^(-1)` `M^2 L^3 T^(-5) A^(-3)` `:. LHS =! RHS, dimensionally.` Hence option (b) is incorrect. (c ) `I = epsilon_0 cV` `A = M^(-1) L^(-3) T^4 A^2 xx LT^(-1)xxML^2 T^(-3) A^(-1) = A` L.H.S. = R.H.S., dimensionally. Hence option (c ) is correct. (d) `mu_0 cI = epsilon_0 V` `M^1 L^1 T^(-2) A^(-2) xx LT^(-1) xxA` `=M^(-1) L^(-3) T^4A^2 xx ML^2 T^(-3) A^(-1)` `M^1 L^2 T^(-3)A^(-1) =! M^0 L^(-1) T^1 A^1` L.H.S =! R.H.S. Hence option (d) is incorrect.