Electrostatics 3 Question 13

13. An infinitely long thin non-conducting wire is parallel to the Z-axis and carries a uniform line charge density λ. It pierces a thin non-conducting spherical shell of radius R in such a way that the arcPQ subtends an angle 120 at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ε0. Which of the following statements is (are) true? (2018 Adv.)

(a) The electric flux through the shell is 3Rλ/ε0

(b) The z-component of the electric field is zero at all the points on the surface of the shell

(c) The electric flux through the shell is 2Rλ/ε0

(d) The electric field is normal to the surface of the shell at all points

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Answer:

Correct Answer: 13. (c, d)

Solution:

  1. PQ=(2)Rsin60

=(2R)32=(3R)qenclosed =λ(3R) We have, φ=qenclosed ε0φ=3λRε0

Also, electric field is perpendicular to wire, so Z-component will be zero.



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