Question

For a finite line charge, find the electric field in a direction parallel to the axis of the line charge at point $\text{P}$.

• A. $6.4\text{N/C}$
• B. $3.4\text{N/C}$
• C. $5.4\text{N/C}$
• D. $4.4\text{N/C}$

Answer 1

The correct option is A $6.4\text{N/C}$

Given:
$r=3\text{m};\lambda =20\text{nC/m}=20\times {10}^{-9}\text{C/m}$


From Pythagoras theorem, in $\Delta \text{PAC}$ and $\Delta \text{PBC}$,

$\text{AP}=5\text{m}$ and $\text{BP}=3\sqrt{2}\text{m}$

So, $\cos \alpha =\frac{3}{5}$ and $\cos \beta =\frac{1}{\sqrt{2}}$

We know that, the electric field at non-axial point $\text{P}$ parallel to line charge axis

$E_{||}=\frac{kQ}{Lr}[\cos \beta -\cos \alpha ]$

$\Rightarrow E_{||}=\frac{k\lambda }{r}[\cos \beta -\cos \alpha ](\because \lambda =Q/L)$

$\Rightarrow E_{||}=\frac{9\times {10}^9\times 20\times {10}^{-9}}{3}[\frac{1}{\sqrt{2}}-\frac{3}{5}]$

$\Rightarrow E_{||}=6.4\text{N/C}$

Hence, option $\left(d\right)$ is correct.