Question

From a finite line charge, the net electric field at the point $\text{P}$ on the equatorial line is equal to

• A. $16.8\text{N/C}$
• B. $31.8\text{N/C}$
• C. $45.8\text{N/C}$
• D. $61.8\text{N/C}$

Answer 1

The correct option is B $31.8\text{N/C}$

Given:
$r=4\text{m};\lambda =10\text{nC/m}=10\times {10}^{-9}\text{C/m}$

From above figure,
$\tan \theta =\frac{4}{4}=1$

$\Rightarrow \theta =\beta ={45}^{\circ }$

We know that, the net electric field at an equatorial point of the uniformly distributed line charge

$E_{\text{net}}=\frac{kQ}{Lr}(\sin \theta +\sin \beta )=\frac{2k\lambda \sin \theta }{r}$

$\Rightarrow E_{\text{net}}=\frac{2\times 9\times {10}^9\times 10\times {10}^{-9}\times \sin {45}^{\circ }}{4}$

$\Rightarrow E_{net}=31.8\text{N/C}$

Hence, option $\left(b\right)$ is the correct answer.