Engineering
Physics
Electric Flux and Gauss Law and its Applications
Question

A charged shell of radius R carries a total charge Given φ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct ?

[∈0 is the permittivity of free space]

If h<8R5    and  r=3R5 then φ = 0

If h > 2R and r=4R5   then  Φ=Q5∈0

If h > 2R and r=3R5  then  Φ=Q5∈0

If h > 2R and r > R then Φ=Q∈0

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Solution

For option (A), cylinder encloses the shell, thus option is correct

For option (B),

 

cylinder perfectly enclosed by shell,

thus φ = 0, so option is correct.

For option (C)

 

φ=2 × Q2∈0 (1−cos 53°)=2Q5 ∈0

For option (D) :

Flux enclosed by cylinder = φ=2Q2∈0(1−cos 37°)=Q5∈0