Question

The electric field in a region is given by $E=\frac{A}{x^{3}}\,\hat{i}+By\,\hat{j}+Cz^{2}\,\hat{k}$ The $SI$ units of $A$ , $B$ and $C$ are, respectively

• A. $\frac{N\,m^{3}}{C}$ , $V/m^{2}$ , $\frac{N}{m^{2}-C}$
• B. $Vm^{2}$ , $V/m$ , $\frac{N}{m^{2}\,C}$
• C. $V/m^{2}$ , $V/m$ , $\frac{N\,C}{m^{2}}$
• D. $V/m$ , $\frac{Nm^{3}}{C}$ , $\frac{NC}{m}$

Answer 1

Answer: (A)

$\frac{N\,m^{3}}{C}$ , $V/m^{2}$ , $\frac{N}{m^{2}-C}$

Answer 2

Here $A, B$ and $C$ must have same unit as of electric field.
So, $\frac{A}{x^3} = \frac{N}{C}$
$\Rightarrow \frac{A}{m^3} \equiv \frac{N}{C}$
$\Rightarrow A \equiv \frac{N - m^3}{C}$
and $By = \frac{V}{m}$
$\Rightarrow Bm \equiv \frac{V}{m^2}$
$\Rightarrow B \equiv \frac{V}{m^2}$
and $Cz^2 \equiv \frac{N}{C}$
$\Rightarrow Cm^2 \equiv \frac{N}{C}$
$\Rightarrow C \equiv \frac{N}{C - m^2}$