Electrostatics Question 739
Question: A uniformly charged and infinitely long line having a linear charge density $ \lambda $ is placed at a normal distance y from a point O. Consider an imaginary sphere of radius R with O as center and R>y. Electric flux through the surface of the sphere is
Options:
A) zero
B) $ \frac{2\lambda R}{{\varepsilon _{0}}} $
C) $ \frac{2\lambda \sqrt{R^{2}-y^{2}}}{{\varepsilon _{0}}} $
D) $ \frac{\lambda \sqrt{R^{2}+y^{2}}}{{\varepsilon _{0}}} $
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Answer:
Correct Answer: C
Solution:
[c] Charge on length $ AB=2\sqrt{R^{2}-y^{2}}\times \lambda $
Electric flux $ \int _{\vec{E}.\overrightarrow{ds}}=\frac{2\lambda \sqrt{R^{2}-y^{2}}}{{\varepsilon _{0}}} $
