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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 PQ 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?
  • a)
    The electric flux through the shell is 
  • 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 
  • d)
    The electric field is normal to the surface of the shell at all points
Correct answer is option 'A,B'. Can you explain this answer?
Verified Answer
An infinitely long thin non-conducting wire is parallel to the z-axis ...
Consider the diagram.

Use trigonometry to find PQ.
PQ = 2PM
= 2Rsin60°

The charge enclosed by the portion of wire PQ is given by,

Apply Gauss law,

This flux points radially outward from the wire so that the electric field in the direction of z-component is zero and also it is normal to the wire, not to the spherical shell.
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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 PQ 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?a)The electric flux through the shell isb)The z-component of the electric field is zero at all the points on the surface of the shellc)The electric flux through the shell isd)The electric field is normal to the surface of the shell at all pointsCorrect answer is option 'A,B'. Can you explain this answer?
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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 PQ 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?a)The electric flux through the shell isb)The z-component of the electric field is zero at all the points on the surface of the shellc)The electric flux through the shell isd)The electric field is normal to the surface of the shell at all pointsCorrect answer is option 'A,B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 PQ 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?a)The electric flux through the shell isb)The z-component of the electric field is zero at all the points on the surface of the shellc)The electric flux through the shell isd)The electric field is normal to the surface of the shell at all pointsCorrect answer is option 'A,B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 PQ 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?a)The electric flux through the shell isb)The z-component of the electric field is zero at all the points on the surface of the shellc)The electric flux through the shell isd)The electric field is normal to the surface of the shell at all pointsCorrect answer is option 'A,B'. Can you explain this answer?.
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