Question

Electric field in a certain region is given by $\overrightarrow{ E }=\left(\frac{ A }{x^2} \hat{i}+\frac{ B }{y^3} \hat{j}\right)$ The $SI$ unit of $A$ and $B$ are :

• A. $Nm ^2 C ^{-1} ; Nm ^3 C ^{-1}$
• B. $Nm ^3 C ; Nm ^2 C$
• C. $Nm ^2 C ; Nm ^3 C$
• D. $Nm ^3 C ^{-1} ; Nm ^2 C ^{-1}$

Answer 1

The Correct Option is A

Equations with Proper Units

Equation 1:

\[ E = x^2 \hat{i} + y^3 \hat{j} \]

Units of A and B:

The unit of \( [A] \) is derived as:

\[ [x^2 A] = \text{NC}^{-1} \quad \Rightarrow \quad [A] = \text{Nm}^2 \, \text{C}^{-1} \]

The unit of \( [B] \) is derived as:

\[ [y^3 B] = \text{NC}^{-1} \quad \Rightarrow \quad [B] = \text{Nm}^3 \, \text{C}^{-1} \]