A charged shell of radius R carries a total charge Q. 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 ? [ε₀ is the permittivity of free space]
Select all that apply

Question

A charged shell of radius R carries a total charge Q. 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 ? [ε₀ is the permittivity of free space]

Select all that apply

G1 Physics · Accepted Answer

Step 1: Flux through any closed surface is enclosed charge/ε₀. If h>2R and r>R, the cylinder contains the entire shell, so Φ=Q/ε₀ (A). Step 2: For r=3R/5 and sufficiently small h<8R/5, the cylindrical surface does not enclose any shell charge, so Φ=0 (B). Step 3: For h>2R, the enclosed shell area fraction is set by the polar cap cut by radius r. At r=3R/5 the enclosed charge is Q/5, so D is correct; r=4R/5 does not give Q/5. Final: A, B, D.