Electric Charges and Fields - Result Question 13
13. Two parallel infinite line charges with linear charge densities $+\lambda C / m$ and $-\lambda C / m$ are placed at a distance of $2 R$ in free space. What is the electric field mid-way between the two line charges?
[2019]
(a) zero
(b) $\frac{2 \lambda}{\pi \in_0 R} N / C$
(c) $\frac{\lambda}{\pi \in_0 R} N / C$
(d) $\frac{\lambda}{2 \pi \varepsilon_0 R} N / C$
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Answer:
Correct Answer: 13. (c)
Solution:
- (c) Electric field due to line charge (1)
$ \overrightarrow{{}E}_1=\frac{\lambda}{2 \pi \varepsilon_0 R} \hat{i} N / C $
Electric field due to line charge (2)
$ \begin{aligned} & \overrightarrow{{}E}_2=\frac{\lambda}{2 \pi \varepsilon_0 R} \hat{i} N / C \\ & \overrightarrow{{}E} _{\text{net }}=\overrightarrow{{}E}_1+\overrightarrow{{}E}_2 \\ & =\frac{\lambda}{2 \pi \varepsilon_0 R} \hat{i}+\frac{\lambda}{2 \pi \varepsilon_0 R} \hat{i} \\ & =\frac{\lambda}{\pi \varepsilon_0 R} \hat{i} / C \end{aligned} $
Both $\overrightarrow{{}E}_1$ and $\overrightarrow{{}E}_2$ are in the same direction.
Electric field at a point due to $+v e$ charge $(+q)$ acts away from the charge and due to negative charge $(-q)$ it acts towards the charge.
