Physics - Unit & Dimension Question with Solution | TestHub

$\overrightarrow{E}=\frac{A}{x^2}\hat{i}+\frac{B}{y^3}\hat{j}$

Here, the units of  $\frac{A}{x^2}$ and $\frac{B}{y^3}$ is equal to unit of electric field.

The unit of electric field is $\mathrm{N} {\mathrm{C}}^{-1}$.

So, the SI unit of $A$ is  $\left[\frac{A}{x^2}\right]=\mathrm{N} {\mathrm{C}}^{-1}\Rightarrow \left[A\right]=\mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-1}$

And the SI unit of $B$ is $\left[\frac{B}{y^3}\right]=\mathrm{N} {\mathrm{C}}^{-1}\Rightarrow \left[B\right]=\mathrm{N} {\mathrm{m}}^3 {\mathrm{C}}^{-1}$