A) zero
B) \[\frac{2\lambda }{\pi {{\varepsilon }_{0}}R}\]
C) \[\frac{\lambda }{\pi {{\varepsilon }_{0}}R}\]
D) \[\frac{1}{2\pi {{\varepsilon }_{0}}R}\]
Correct Answer: B
Solution :
According to Gausss theorem \[\phi =\frac{q}{{{\varepsilon }_{0}}}\] or \[E.2\pi R\times l=\frac{\lambda }{{{\varepsilon }_{0}}}\] \[\Rightarrow \] \[E=\frac{1}{2\pi }\frac{\lambda }{{{\varepsilon }_{0}}(R/2)}\times 2\] \[(l=1)\] \[=\frac{2\lambda }{\pi {{\varepsilon }_{0}}R}\]
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