Question

A point charge q is placed at origin. Let $\overrightarrow{E_A},\overrightarrow{E_B}$ and $\overrightarrow{E_C}$ be the electric fields at three points $A(1,2,3),B(1,1,-1)$ and $C(2,2,2)$ due to charge q. Then :

• A. $\overrightarrow{E_A}\perp \overrightarrow{E_B}$
• B. $\overrightarrow{E_A}=\overrightarrow{E_B}$
• C. $\left|\overrightarrow{E_B}\right|=\left|\overrightarrow{E_C}\right|$
• D. $\left|\overrightarrow{E_B}\right|=8\left|\overrightarrow{E_C}\right|$

Answer 1

The correct option is A $\overrightarrow{E_A}\perp \overrightarrow{E_B}$

The direction of electric field is in the direction of the vector joining the origin and the point where the electric field is to be found (charge is assumed to be positive and is kept at origin).
In first case direction of E $=\hat{i}+2\hat{j}+3\hat{k}$
In second case direction of E $=\hat{i}+\hat{j}-\hat{k}$
These two vectors are perpendicular as their dot product is 0.