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

The Correct Option is A

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 $Cz^2 \equiv \frac{N}{C}$
$\Rightarrow Cm^2 \equiv \frac{N}{C}$
$\Rightarrow C \equiv \frac{N}{C - m^2}$