Question

In terms of potential difference V, electric current I, permitivity `epsi_(0)`, permeability `mu_(0)` and speed of light c, the dimensionally correct equations (s) is (are) :
A. `mu_(0)I_(2)=epsiV^(2)`
B. `mu_(0)I=mu_(0)V`
C. `I=epsi_(0)V`
D. `mu_(0)cI=epsi_(0)V`

Answer 1

Correct Answer - a, c
`[V]=[M^(1)L^(2)T^(-3)A^(-1)]`
`[I]=[A]`
`[c]=[L^(1)T^(-1)]`
`[epsi_(0)]=[M^(-1)L^(-3)T^(4)A^(2)]`
`[mu_(0)]=[M^(-1)L^(1)T^(-2)A^(-2)]`
Option (a) :
`[mu_(0)I^(2)]=[M^(1)L^(1)T^(-2)]`
`[E_(0)V^(2)]=[M^(1)L^(1)T^(-1)]`
Option (b) :
`[epsi_(0)I]=[M^(1)L^(-3)T^(4)A^(3)]`
`[mu_(0)V]=[M^(2)L^(3)T^(-5)A^(-3)]`
Option (c) :
`[I]=[A]`
`[epsi_(0)cV]=[A]`
Option (d) :
`[mu_(0)cI]=[M^(1)L^(2)T^(-3)A^(-1)]`
`[epsi_(0)V]=[L^(-1)TA]`
Options (a) and (c) correct.