Transcript Ch. 21 ElectricForcesFields

Ch. 21 Electric Forces
& Fields
AP Physics C
1. Pith Ball Lab Sample Problem
Problem 2:
• An electrically neutral penny, of
mass 3.11 g, contains equal
amounts of positive and negative
charge. Assuming the penny is
made entirely of copper, what is
the magnitude q of the total
positive (or negative charge)
charge in the penny?
• http://www.webelements.com/
Problem 3:
• The average distance between the
electron and the central proton in
the hydrogen atom is 5.3 x 10-11 m.
• What is the magnitude of the
average electrostatic force that
acts between these two particles?
• What is the magnitude of the
average gravitational force that
acts between these particles?
Charges & Fields:
• http://phet.colorado.ed
u/simulations/sims.php?si
m=Charges_and_Fields
• Electric field:
Oppositedly
charged parallel
plates
Problem 6:
• The diagram below shows a
charge +8q at the origin of an xaxis and a charge of -2q at x = L.
At which points is the net electric
field due to these two charges
zero?
Problem 7:
• The nucleus of a uranium atom has
a radius R of 6.8 fm. Assuming that
the positive charge of the nucleus
is distributed uniformly, determine
the electric field at a point on the
surface of the nucleus due to that
charge. (Note: 1 fm = 1 x 10-15 m;
The atomic mass unit for uranium is
92.)
Continuous distribution of charge:
• Electric Field due to a continuous
distribution of charge:
• Charge per unit length:
dq

ds
dq
• Charge per unit surface:   dA
• Charge per unit volume:

dq
dV
A ring of uniform positive charge
•
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizatio
ns/electrostatics/09RingIntegration/RingIntegrationFullScreen.htm
• Through the use of
integration, determine
the total electric field at a
point that is x from the
center of a continuous
ring of positive charge, Q,
that has a radius of R.
Problem 10:
• A plastic rod having a uniformly distributed charge of –Q.
The rod has been bent in a 120o circular arc of radius r.
The coordinate axes are placed such that the axis of
symmetry of the rod lies along the x-axis and the origin is
at the center of curvature of the rod. In terms of Q and r,
what is the electric field due to the rod at the origin of the
axes?
Problem 11:
• In the Millikan’s oil-drop
apparatus, a drop of
radius 2.76 μm has an
excess charge of three
electrons. What are the
magnitude and direction
of the electric field that is
required to balance the
drop so it remains
stationary in the
apparatus? The density
of the oil is 920 kg/m3.
Problem 12:
• Determine the path
that the proton will
follow.
• If the proton is
entering the electric
field of 10 N/C at the
positive plate, how
far does it move
vertically if the plates
are 10 cm long?
Applications of uniform electric fields:
Ink-Jet Printer
Cathode-Ray Tube
13. Electric dipole in a uniform E-Field
• What is the net
force acting on
the dipole?
• What is the net
torque about the
center of the rod?
13. Electric dipole in a uniform E-Field
• The dipole
moment, p, is
define to be:
• p = qd, where d =
L.
• Its direction is from
the net negative
charge towards
the net positive
charge.
13. Potential energy of an electric
dipole
• The potential energy of
an electric dipole is
associated with the
orientation of the electric
dipole in an electric field.
13. Potential energy of an electric
dipole
• The dipole is at its lowest
potential energy when it
is in its equilibrium
orientation, which is
when its moment p is
parallel with the E-field
and the torque is zero.
• This position is called
stable equilibrium.
13. Potential energy of an electric
dipole
• Its greatest potential
energy is when p is
perpendicular to the Efield and the torque has a
maximum value.
• This is referred to as an
unstable equilibrium
position.
13. Work done by the external field
on the dipole
2
U  W     d
1
2
U  W    pE sin  d
1
U   pE[ cos  2  ( cos 1 )]
• Potential is defined as:
U   pE cos    p  E
Problem 14:
• A neutral water molecule in its vapor state has an
electric dipole moment of 6.2 x 10-30 C-m.
• How far apart are the molecule’s centers of
positive and negative charge?
• If the molecule is placed in an electric field of
1.5 x 104 N/C, what maximum torque can the
field exert on it?
• How much work must an external agent do to
turn this molecule end for end in this field,
starting from its fully aligned position, for which θ
= 0?