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An infinitely long thin non-conduction w...

An infinitely long thin non-conduction wire is parallel to the z-axis and carries a uniform line charge density `lambda`. It pierces a thin non-conducting spherical shell of radius r in such a way that that the are PQ subtends an angle `120^(@)` at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is `epsi_(0)`. which of the following statements is (are) true ?

A

The electric flux through the shell is `sqrt(3) R lambda // epsi_(0)`

B

The z -component of the electric field is zero at all the point on the surface of the shell

C

The electric flux thourgh the shell is `sqrt(2)R lambda // in_(0)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A, B
Flux through shell is
`phi=(q_(enc))/(epsi_(0))=(lamda(2Rsin60^(@))/(in_(0))=(sqrt3lamdaR)/(in_(0))` (A is correct)
Field due to infinite charged wire is perpendicular to the wire
`thereforeE_(z)=0` at all points (B is correct)
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