Question

The electric field intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance rir r(r > R) from its axis is ______.

Options

• directly proportional to r².

• directly proportional to r³.

• inversely proportional to r.

• inversely proportional to r².

Answer 1

The electric field intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance rir r(r > R) from its axis is inversely proportional to r.

Explanation:

`oint vec"E"*vec"ds" = oint "ds" = 2pi"r"l"e"`

According to Gauss's law (E is constant)

`"E" * 2pi"rl" = "ql"/epsilon_0 "or" "E" = "q"/(2piepsilon_0"r")`

i.e. `"E" prop 1/"r"`