Download The charged ball attached to the string is the point charge. Visualize

25.69. Model: The charged ball attached to the string is the point charge.
Visualize:
The charged ball is in static equilibrium in the external electric field when the string makes an angle θ with the
vertical. The three forces acting on the charge are the electric force due to the electric field, the weight of the ball,
and the tension force.
r
r r r r
Solve: In static equilibrium, Newton’s second law for the charged ball is Fnet = T + w + F3 = 0 . In component
form,
( Fnet ) x = Tx + 0 N + qE = 0 N
( Fnet ) y = Ty − mg + 0 N = 0 N
These two equations become T sin θ = qE and T cosθ = mg . Dividing the equations gives
tan θ =
−9
qE (25 × 10 C)(200,000 N / C)
=
= 0.255 ⇒ θ = 14.3°
mg
(2.0 × 10 −3 kg)(9.8 N / kg)