Question

A thread carrying a uniform charge $\lambda$ per unit length has the configuration shown in figures. Assuming a curvature radius R to be considerably less than the length of the thread, find the magnitude of the electric field strength at the point O.

• A. Zero, zero
• B. $\frac{\sqrt{2}k\lambda }{R},zero$
• C. $Zero,\frac{\sqrt{2k\lambda }}{R}$
• D. $\frac{\sqrt{2}k\lambda }{R},\frac{\sqrt{2}k\lambda }{R}$

Answer 1

The correct option is B $\frac{\sqrt{2}k\lambda }{R},zero$

(a)

$\overrightarrow{E}=\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}$
$=\frac{k\lambda }{R}(\hat{i}-\hat{j})+\frac{k\lambda }{R}(\widehat{+i}+\hat{j})+\frac{k\lambda }{R}(\widehat{-i}+\hat{j})$
$=\frac{k\lambda }{R}(\hat{i}+\hat{j})$
$=\frac{\sqrt{2}k\lambda }{R}$

(b)

$\overrightarrow{E}=\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}$
$=\frac{k\lambda }{R}(\hat{i}-\hat{j})+\frac{2k\lambda }{R}\left(\hat{j}\right)+\frac{k\lambda }{R}(\widehat{-i}-\hat{j})$
$=\frac{k\lambda }{R}[\hat{i}-\hat{j}+2\hat{j}-\hat{i}-\hat{j}]=0$