In the fromla `X = 1 YZ^(2)`, `X` and `Z` have dimensions of capacitance and amgnetic induction, respectively. The dimension of `Y` in `MKSQ` system are

Options

A. `M^(-3) L^(-2) T^(4) Q^(4)`
B. `M^(-1) L^(-3) T^(4) Q^(4)`
C. `M^(-3) L^(-2) T^(2) Q^(4)`
D. `M^(-3) L^(-2) T^(2) Q^(4)`

Answer

A

Explanation

(1) `Y = (X)/(3 Z^(2)) : (farad)/((n e w t o n//amp. M)^(2)) = (c o u l//v o l t)/((n e w t o n//amp.m)^(2))`
`= (c o u l. c o u l. (amp . M)^(2))/(j o u l e (n e w t o n)^(2)) = ((c o u l)^(2) (c o u l)^(2) (m)^(2))/((j o u l e) (n e w t o n)^(2) s^(2))`
`= (Q^(4) L^(2))/(ML^(2) T^(-2) (MLT^(-2))^(2) T^(2))`
`= (Q^(4) L^(2))/(M^(3) L^(4) T^(-4)) = M^(-3) L^(-2) T^(4) Q^(4)`