496
11 Electrostatics
Fig. 11.30
11.29 The electric force F e = the gravitational force
q 2
4πε 0 r 2 =
Gm 2
r 2
q
m
= (4πε 0 G)
1/2
=
6.67 × 10 −11
9 × 10 9
1/2
= 8.65 × 10
−9 C/kg
11.30 Consider the equilibrium of one of the spheres, Fig. 11.31. If T is the tension
in the string then
T cos θ = mg
T sin θ =
q 2
4πε 0 x 2
∴
tan θ θ =
x
2L
=
q 2
4πε 0 mgx 2
∴
q =
2πε 0 mg
L
1/2
x
3/2
Fig. 11.31
11 Electrostatics
Fig. 11.30
11.29 The electric force F e = the gravitational force
q 2
4πε 0 r 2 =
Gm 2
r 2
q
m
= (4πε 0 G)
1/2
=
6.67 × 10 −11
9 × 10 9
1/2
= 8.65 × 10
−9 C/kg
11.30 Consider the equilibrium of one of the spheres, Fig. 11.31. If T is the tension
in the string then
T cos θ = mg
T sin θ =
q 2
4πε 0 x 2
∴
tan θ θ =
x
2L
=
q 2
4πε 0 mgx 2
∴
q =
2πε 0 mg
L
1/2
x
3/2
Fig. 11.31