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Q.

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?

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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

answer is A.

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Detailed Solution

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=λ3R∈0∵Linear charge density, λ=ql⇒q=λl=λ(PQ)

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