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 ε$$0$$. Which of the following statements is (are) true?

Question

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 ε$$0$$. Which of the following statements is (are) true?

Infinity Learn · Accepted Answer

Filed due to straight wire is perpendicular to the wire & radially outward. Hence  $$Ez=0$$ .Length,  $$PQ=2R$$ $$sin60=3R$$ According to gauss’s lawTotal $$flux=$$ ∮E→.ds→$$=qin$$∈$$0=$$λ$$3R$$∈$$0$$∵Linear charge density, λ$$=ql$$⇒$$q=$$λ$$l=$$λ(PQ)

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material