Bukhovtsev-et-al-Problems-in-Elementary-Physics

ELECTRICITY AND MAGNETISM
295
Fig. 409 Fig. 410
where T 1 and T 2 are the tensions of the thread, al and ~ the angles of
deflection of the thread, + Q and ~ Q the charges of the fixed balls, + Qs
the charge of the suspended ball, and mg is the weight of the suspended
ball (Fig. 409).
Upon excluding the unknowns from the above simultaneous equations, we
get
cot a 1 -cot a 2=cot ai-cot 2al =2(V2-1)
whence,
cot al=2 (2 Y2 - 1) ± V35-16 Y 2
Thus, C&J. =7°56' and a,=15°52' when mg > ~~s ( 1--':2 ), and
al=82°04' and a 2=164°OB' when mg < ~~s (1--':2 ).
399. In uniform motion the drop is acted upon by the force of gravity G.
the expulsive force of the air (Archimedean force) F, the force of the electrostatic
field eE and the force of friction against the air kv=k ~ . All the forces
are balanced. Therefore,
G-F-eEO+k..!..=O
t 1
G-F+eE-k~=O
t;
G-F-k!..=O
t
where e is the charge of the drop, E the intensity of the electric field, and s
the distance covered by the drop.