Sample Problem Gauss Law
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 These electrons come from the cloud and from air molecules that are ionized within the column. The linear charge density A along the column is typically -I X 10′ elm. Once the column reaches the ground. electrons within it are rapidly dumped to the ground During the dumping. collisions bel ween the moving electrons and the air within the column result in a brilliant flash of light If air molecules break down (ionize) in an electric field exceeding 3 x 106 N/C what i the radius of the column One Key Idea here is that. although the column is not straight or infinitely long can approximate it as being a line of charge as in Since it contains a net negative charge.
(The radius of the luminous portion of a lightning strike is smaller perhaps only 0.5 m. You can get an idea of the width from Although the radius of the column may be only 6 m do not assume that you are safe if you are at a somewhat greater distance from the strike point, because the electrons dumped by the strike travel along the ground Such ground currents are lethal shows evidence of ground currents Lightning strikes a 20-m-high sycamore Because the tree was wet, most of the charge traveled through the water on it and the tree was unharmed its electric field f points radially inward Then according to the field’s magnitude E decreases with distance from the axis of the column of charge A second Key Idea is that the surface of the column of charge must be at the radius r where the magnitude of f is 3 X 10′ N/C. because air molecules within that radius ionize farther Ground currents from a lightning strike have burned rass off this golf green exposing the soil.