Electric field in a certain region is given by overrightarrow{ E }=left(frac{ A }{ x ^2} hat{ i }+fr

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1.Units, Dimensions and Measurement

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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

$Nm ^3\,C ^{-1} ; Nm ^2 \,C ^{-1}$

B

$Nm ^2\, C ^{-1} ; Nm ^3 \,C ^{-1}$

C

$Nm ^3 \,C ; Nm ^2 \,C$

D

$Nm ^2 \,C ; Nm ^3\, C$

(JEE MAIN-2023)

Solution

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

${\left[\frac{ A }{ x ^2}\right]= NC ^{-1} \Rightarrow[ A ]= Nm ^2 C ^{-1}}$

${\left[\frac{ B }{ y ^3}\right]= NC ^{-1} \Rightarrow[ B ]= Nm ^3 C ^{-1}}$

Standard 11

Physics

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