The visible portion of a lightning strike is preceded by an invisible stage in which a column of electrons extends downward from a cloud to the ground Assume the linear charge density along the column is `1.00xx10^(-3)C//m` Treat the column of charge as if it were straight and infinitely long. At what distance (in m) from the column of electrons does the electric field have a magnitude of `3.00xx10^(6) V//m` the dielectric strength for air? This is an estimate of the radius of a visible lightning bolt. (Round off to nearest integer) (value of `in_(0)is 8.85xx10^(-12) C^(2)//Nm^(2))`

Answer

`6 m`

Explanation

`lambda/(2pi in_(0)r)=E_(break)`
`r=lambda/(2piin_(0)E_(break))`
`=10^(-3)/(2xx3.14xx8.85xx10^(-12)xx3xx10^(6))`
`=1/(2xx3.14xx8.85)xx10^(3)`
`=5.99m approx 6m`