Question

Deduce the dimensional equation of self-inductance. 
 

Hint:

The dimensional formula of self-inductance is \( \left[ \text{M} \text{L}^2 \text{T}^{-2} \text{A}^{-2} \right] \).

Answer 1

Self-inductance (\( L \)) is defined by the relation: \[ \text{Emf} = -L \frac{dI}{dt}, \] where \( \text{Emf} \) is the induced electromotive force and \( I \) is the current. The dimensional formula of \( \text{Emf} \) is: \[ \left[ \text{Emf} \right] = \left[ \frac{\text{ML}^2}{\text{T}^3 \text{A}} \right]. \] By substituting the dimensional formula of \( \frac{dI}{dt} \) (which is \( \text{T}^{-1} \text{A} \)): \[ \left[L \right] = \frac{\left[ \text{Emf} \right]}{\left[ \frac{dI}{dt} \right]} = \frac{\left[ \text{ML}^2 \right]}{\left[ \text{T}^3 \text{A} \right] \times \left[ \text{T}^{-1} \text{A} \right]} = \left[ \text{M} \text{L}^2 \text{T}^{-2} \text{A}^{-2} \right]. \]