252 Aptitude Test Problems in Physics(We assume that the charge and the potential of
the large sphere change insignificantly in each
charging of the balls.) When the large sphere is
connected to the third ball, the first and second
balls being charged, the equation describing the
equality of potentials has the form
4neo (^) f / d d
The charge q 3 can be found by solving the system
of equations (1)-(3):
n 2
q 3 = V2
q1 •
3.9. The charge qi of the sphere can be determined
from the formula
q1 = 4 n 8 0(P1r1•
After the connection of the sphere to the envelope,
the entire charge q^1 will flow from the sphere to the
envelope and will be distributed uniformly over
its surface. Its potential (p 2 (coinciding with the
new value of the potential of the sphere) will be
ql
r1
4neor2= (Pi r^ •
2
3.10. We shall write the condition of the equality
to zero of the potential of the sphere, and hence
of any point inside it (in particular, its centre), by
the moment of time t. We shall single out three
time intervals:
(1) t <
a
-- , (2) - a — t < , (3) t --
v v
Denoting the charge of the sphere by q (t), we obtain
the following expression for an instant t from the
first time interval:
(^91 42) q (t) =o
a b (^) ut