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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 arc P Q subtends an angle 120 o at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ϵ 0 . Which of the following statements is (are) true?

Options

  1. AThe electric flux through the shell is 3 R λ / ϵ 0
  2. BThe z - component of the electric field is zero at all the points on the surface of the shell
  3. CThe electric flux through the shell is 2 R λ / ϵ 0
  4. DThe electric field is normal to the surface of the shell at all points

Correct answer

A. The electric flux through the shell is 3 R λ / ϵ 0

Step-by-step solution

Field due to straight wire is perpendicular to the wire and radially outward. Hence E z = 0 Length, P Q = 2 R sin ⁡ 60 = 3 R According to Gauss's law Total flux = ∮ E → . d s → = q i n ∈ 0 = λ 3 R ∈ 0

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