Question

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