91. (a) Suppose the pendulum is at the angle
θ
with the vertical. The force diagram is
shown below.
G
T
is the tension in the thread,
mg
is the magnitude of the force of gravity,
and
qE
is the magnitude of the electric force. The field points upward and the charge is
positive, so the force is upward. Taking the angle shown to be positive, then the torque on
the sphere about the point where the thread is attached to the upper plate is
(
)
sin
mg
qE L
τ
θ
= −
−
.
If
mg
>
qE
then the torque is a restoring torque; it tends to pull
the pendulum back to its equilibrium position.
If the amplitude of the oscillation is small, sin
θ
can be replaced by
θ
in radians and the
torque is
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 Fall '10
 Rebello,NobelS
 Force, Gravity, Simple Harmonic Motion, Electric charge, Fundamental physics concepts, mg − qE

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