Question

What is the dimensional formula for magnetic flux?

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

Answer 1

Answer: (A)

Magnetic flux is given as $\phi=B S \cos \theta$ ...(i)
Here is $B$ magnetic field and $S$ is area.
Magnetic force $F$ on a charge $q$ moving with velocity $v$ is given as $F=q v B \sin \beta$
So, $B=\frac{F}{q v \sin \beta}$ .............(ii)
By equations (i) and (ii)
$\phi=\frac{F}{q v \sin \beta} \times S \cos \theta$
Trigonometric functions are dimensionless
so
$\phi=\frac{F S}{q v}=\frac{M L T^{-2} \times L^{2}}{A T \times L T^{-1}}=M L^{2} T^{-2} A^{-1}$