11.3 Solutions
507
For a non-conducting sheet the field
E =
σ
2ε 0
(1)
The electric force acting on the sphere is
F = q E =
qσ
2ε 0
(2)
(c) The sphere is held in equilibrium under the joint action of three forces:
(1) Weight acting vertically down,
(2) Electric force F acting horizontally, and
(3) Tension in the thread acting along the thread at an angle θ with the
vertical.
From Fig. 11.42, F/mg = tan θ
(3)
Combining (2) and (3)
σ =
2ε 0 mg tan θ
q
=
2 × 8.9 × 10 −12 × 2 × 10 −6 × 9.8 × tan 10 ◦
5 × 10 −8
= 2.15 × 10
−11 C/m
2
Fig. 11.42
507
For a non-conducting sheet the field
E =
σ
2ε 0
(1)
The electric force acting on the sphere is
F = q E =
qσ
2ε 0
(2)
(c) The sphere is held in equilibrium under the joint action of three forces:
(1) Weight acting vertically down,
(2) Electric force F acting horizontally, and
(3) Tension in the thread acting along the thread at an angle θ with the
vertical.
From Fig. 11.42, F/mg = tan θ
(3)
Combining (2) and (3)
σ =
2ε 0 mg tan θ
q
=
2 × 8.9 × 10 −12 × 2 × 10 −6 × 9.8 × tan 10 ◦
5 × 10 −8
= 2.15 × 10
−11 C/m
2
Fig. 11.42