Question

The electric potential existing in space is $V(x,y,z)=A(xy+yz+zx)$. Write the dimensional formula of $A$ :

• A. $M{T}^{-2}{I}^{-1}$
• B. $M{T}^{-3}{I}^{-1}$
• C. $M{T}^{-2}{I}^{-2}$
• D. $M{T}^{-3}{I}^{-2}$

Answer 1

Answer: (B)

$M{T}^{-3}{I}^{-1}$

Since $x,y$ and $z$ have units of length i.e. $m$.
Thus Unit of A =unit of potential $\times m^{-2}$ = joules per coulomb $\times m^{-2}$

Dimension of joule $=M{L}^2{T}^{-2}$

Dimension of coulomb $=IT$ where $I$ is the dimension of current.
Dimension of A = dimension of joule per coulomb $\times L^{-2}$
= $M{L}^2{T}^{-2}(IT{)}^{-1}\times L^{-2}=M{T}^{-3}{I}^{-1}$