Question

The electric intensities at a point due to two point charges in the $ x - y $ plane are $3 \hat{i} -2 \hat{j} $ and $ -2\hat{i} +4\hat{j} $ The magnitude of the resultant intensity at that point is

• A. $ 2.08 \,V\,m^{-1} $
• B. $ 2.24 \,V\,m^{-1} $
• C. $ 1.8 \,V\,m^{-1} $
• D. $ 3.5 \,V\,m^{-1} $

Answer 1

The Correct Option is B

Given : $\vec{E}_{1}=3 \hat{i}-2 \hat{j}, \vec{E}_{2}=-2\hat{i}+4\hat{j}$ Resultant electric intensity at given point is $\vec{E}=\vec{E}_{1}+\vec{E}_{2}=\left(3\hat{i}-2 \hat{j}\right)+\left(-2 \hat{i}+4 \hat{j}\right)=\hat{i}+2\hat{j}$ $\left|\vec{E}\right|=\sqrt{\left(1\right)^{2}+\left(2\right)^{2}}$ $=\sqrt{1+4}=\sqrt{5}=2.24\,V\,m^{-1}$