11.3 Solutions
487
ii. For equilibrium, the attractive force must balance the repulsive force:
√
3q 2
4πε 0 a 2 −
3Qq
4πε 0 a 2 = 0 → Q = −q/
√
3
Fig. 11.20
11.11 Referring to Fig. 11.21, the Coulomb force between the spheres in air is
F =
q 2
4πε 0 x 2
In liquid F =
q 2
4πε 0 K x 2 ; weight of the sphere in air = mg
Apparent weight of the sphere in liquid = mg
1 −
ρ
ρ
, where ρ is the
density of the material of sphere and ρ that of the liquid. For equilibrium
the vertical and horizontal components of the force must separately balance.
If T is the tension in the string when the sphere is in air and T when it is in
the liquid,
T sin θ = F, T cos θ = mg
T
sin θ = F
, T
cos θ = mg
1 −
ρ
ρ