Question

The magnitude and direction of the electric field at point $P$ can be best represented by

• A. $\frac{3 k q}{x^{2}}\left(\right.\hat{i}+\hat{j}\left.\right)$
• B. $\frac{\sqrt{2} k q}{x^{2}}\left(\right.\hat{i}+\hat{j}\left.\right)$
• C. $\frac{3 \sqrt{2} k q}{x^{2}}\left(\right.-\hat{i}-\hat{j}\left.\right)$
• D. $\frac{3 \sqrt{2} k q}{x^{2}}\left(\right.\hat{i}+\hat{j}\left.\right)$

Answer 1

Answer: (D)

$\overset{ \rightarrow }{E}_{P}=E′cos45^\circ \hat{i}+E′sin45^\circ \hat{j}$
$= \, E′\left(\frac{\hat{i}}{\sqrt{2}} + \frac{\hat{j}}{\sqrt{2}}\right) \, \, \, = \, \frac{k 3 q}{\left(\frac{x}{\sqrt{2}}\right)^{2}}\left(\frac{\hat{i}}{\sqrt{2}} + \frac{\hat{j}}{\sqrt{2}}\right)$
$= \, \frac{6 k q}{x^{2}}\left(\frac{\hat{i}}{\sqrt{2}} + \frac{\hat{j}}{\sqrt{2}}\right) \, \, = \, \frac{3 \sqrt{2} k q}{x^{2}}\left(\right.\hat{i}+\hat{j}\left.\right)$