Question

The dimensions of the ratio of magnetic flux $(\varphi )$ and permeability $(\mu )$ are

• A. $[M^0{L}^1{T}^0{A}^1]$
• B. $[M^0{L}^{-3}{T}^0{A}^1]$
• C. $[M^0{L}^1{T}^1{A}^{-1}]$
• D. $[M^0{L}^2{T}^0{A}^1]$

Answer 1

Answer: (A)

Magnetic flux $=\varphi =BA,G$ = magnetic field ,A = area
Permeability $=\mu =\frac{B}{H}$ , = magnetic intensity
$\frac{\varphi }{\mu }=\frac{BA}{(\frac{B}{H})}$ Area $\times$ magnetic intensity
[Area ] $=[A]=[L^2]$
Magnetic intensity = H = nI= $=\frac{\text{ number of turns }}{\text{ metre }}\times$ current
$[H]=[\frac{A^{\prime }}{L}]$ [current] = [A']
$\therefore [\frac{\varphi }{\mu }]=[L^2\times \frac{A^{\prime }}{L}]=[L{A}^{\prime }]$
$\therefore [\frac{\varphi }{\mu }]=[M^0{L}^1{T}^0{A}^1]$