Question

A charged shell of radius r carries a total charge q. Given as the flux of the electric field through a closed cylindrical surface of height h, radius r, and with its center same as that of the shell. Here, the 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?

Options:
a. Φ=​q/ε0​
b. Φ=q/2ε0​
c. Φ=​qh/2ε0​
d. Φ=qh/ε0​​

Answer 1

Using Gauss's law, the electric flux through a cylindrical surface around a uniformly charged shell is equal to the total charge on the shell divided by the permittivity of vacuum, regardless of the cylinder's dimensions. Therefore, the correct option is A.

Step-by-step explanation:

The question involves applying Gauss's law to determine the electric flux Φ through a cylindrical surface around a uniformly charged shell. Knowing that the electric field E created by a shell with total charge q is radial and that within the shell (at distances less than the shell's radius r), E is zero, we can deduce the electric flux through surfaces that are wholly inside or outside the shell.

According to Gauss's law, the electric flux Φ through any closed surface surrounding a charge is given by the charge enclosed (qenc) divided by the permittivity of vacuum (ε0). Since the charge enclosed by the cylindrical surface is equal to the total charge q on the shell, independent of the cylinder's height h, the correct answer is Φ = q/ε0, which corresponds to option (a).