Problem 62.60 In problem 24 on p. 660, you estimated the energy released
in a bolt of lightning, based on the energy stored in the electric field
immediately before the lightning occurs. The assumption was that
the field would build up to a certain value, which is what is necessary
to ionize air. However, real-life measurements always seemed to
show electric fields strengths roughly 10 times smaller than those
required in that model. For a long time, it wasn’t clear whether the
field measurements were wrong, or the model was wrong. Research
carried out in 2003 seems to show that the model was wrong. It is
now believed that the final triggering of the bolt of lightning comes
from cosmic rays that enter the atmosphere and ionize some of the
air. If the field is 10 times smaller than the value assumed in problem
24, what effect does this have on the final result of problem 24?√61 A charged particle of massmand chargeqis below a hor-
izontal conducting plane. We wish to find the distancebetween the particle and the plane so that the particle will be in equilibrium, with its weight supported by electrostatic forces. (a) Determine as much as possible about the form of the answer based on units. (b) Find the full result for.
(c) Show that the equilibrium is unstable.
62 A point chargeqis situated in the empty space inside a corner
formed by two perpendicular half-planes made of sheets of metal.
Let the sheets lie in they-z andx-zplanes, so that the charge’s
distances from the planes arexandy. Bothxandyare positive.
The charge will accelerate due to the electrostatic forces exerted by
the sheets. We wish to find the directionθin which it will accelerate,
expressed as an angle counterclockwise from the negativexaxis, so
that 0< θ < π/2.
(a) Determine as much as possible about the form of the answer
based on units.
(b) Find the full result forθ.
Problems 667