Units And Dimensions Question 7
Question 7 - 30 January - Shift 1
Electric field in a certain region is given by $\dot{E}=(\frac{A}{x^{2}} \hat{i}+\frac{B}{y^{3}} \hat{j})$. The SI unit of $A$ and $B$ are :
(1) $Nm^{3} C^{-1} ; Nm^{2} C^{-1}$
(2) $Nm^{2} C^{-1} ; Nm^{3} C^{-1}$
(3) $Nm^{3} C ; Nm^{2} C$
(4) $Nm^{2} C ; Nm^{3} C$
Show Answer
Answer: (2)
Solution:
Formula: Principle of homogeneity of dimensions
$\vec{E}=\frac{A}{x^{2}} \hat{i}+\frac{B}{y^{3}} \hat{j}$
$[\frac{A}{x^{2}}]=NC^{-1} \Rightarrow[A]=Nm^{2} C^{-1}$
