Question

Electric field in a certain region is given by $\vec{ E }=\left(\frac{ A }{x^2} \hat{i}+\frac{ B }{y^3} \hat{j}\right)$. 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

Answer: (A)

$ \vec{ E }=\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j } $
$ {\left[\frac{ A }{ x ^2}\right]= NC ^{-1} \Rightarrow[ A ]= Nm ^2 C ^{-1}} $
${\left[\frac{ B }{ y ^3}\right]= NC ^{-1} \Rightarrow[ B ]= Nm ^3 C ^{-1}}$