Question

Find the dimensional formulae of the following quantities:
(a) the charge `Q`
(b) the permittivity of free space `epsilon_(0)`
(c) the electric field `E`
(d) the electric potential `V`
(e) the capacitance `C`
`Q`=It, `F=(l)/(4piepsilon^(0)).(q_(1)q_(2))/(r^(2)),E=(F)/(q),V=(W)/(q)=CV`
where `I`: current, F: force,`q`: charge, `r`: distance and `W`: work.

Answer 1

(a) `Q=l t`
`[Q] =AT`
(b) `F=(1)/(4piepsilon_(0)) (q_(1)q_(2))/(4pi Fr^(2))`
`[epsilon_(0)] = ([AT]^(2))/(MLT^(-2)L^(2))=M^(-1)L^(-3)T^(4)A^(2)`
( c) `E=(F)/(q)`
`[E]=(MLT^(-2))/(AT)=MLT^(-3)A^(-1)`
(d) `V=(W)/(q)`
`[V] = (ML^(2)T^(-2))/(AT)=ML^(2)T^(-3)A^(-1)`
(e) `q=CVrArrC=(q)/(V)`
`[C]=(AT)/(ML^(2)T^(-3)A^(-1))=M^(-1)L^(-2)T^(4)A^(2)`