Question

Dimensional formula of self inductance is:

• A. $ML{T}^{-2}{A}^{-2}$
• B. $M{L}^2{T}^{-1}{A}^{-2}$
• C. $M{L}^2{T}^{-2}{A}^{-2}$
• D. $M{L}^2{T}^{-2}{A}^{-1}$

Answer 1

The correct option is C $M{L}^2{T}^{-2}{A}^{-2}$

The magnetic flux is given by

$\varphi =LI$

The dimensional formula of self inductance, $\left[L\right]=\frac{\left[BA\right]}{\left[I\right]}$. . . . . .(1)

Force, $f=qvB$

$\left[M^1{L}^1{T}^{-2}\right]=\left[TA\right].\left[L^1{T}^{-1}\right].\left[B\right]$

$\left[B\right]=\left[M^1{T}^{-2}{A}^{-1}\right]$

$\left[BA\right]=\left[M^1{L}^2{T}^{-2}{A}^{-1}\right]$

From equation (1), we get

$\left[\varphi \right]=\left[M^1{L}^2{T}^{-2}{A}^{-2}\right]$

The correct option is C.