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1P22/1P92 Problems (2011) Chapter 21 Electric Potential
Friday, January 14, 2011
10:03 AM
In the previous chapter we learned about the use of the electric field concept to
describe electric forces between charges. In this chapter, we'll learn about the electric
potential (also called "voltage"), which gives us an alternative, complementary, and
useful way to describe electric fields.
Think back to topographical maps, which you might have studied before. Here's an
example:
As we discussed in class, here are the key properties of the topographical map:
• Counter lines represent points of the landscape that have the same height; they also
have the same gravitational potential, so we can call them equipotential lines, or
equipotentials for short.
• If the landscape were perfectly smooth and frictionless, a small particle released on the
landscape would experience a force that is perpendicular to the counter line at the
particle's position.
• The landscape is steepest where the contour lines are closest together (think rise-over
run, which is a way to calculate the slope of the landscape in a certain direction). The
landscape is less steep where the contour lines are farther apart.
Also as we discussed in class, for conservative force fields (such as electric fields), one
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can set up a potential function (analogous to gravitational potential) that shares many
of the properties of contour lines in topographical maps. Translating these properties
into the realm of electric potential functions, here are their key properties:
• Equipotentials represent points in space where the electric potential is constant. (In
three dimensions, the equipotentials are surfaces, not lines.)
• The force experienced by a small charged particle is perpendicular to the equipotential
at the particle's position. Another way to say this is that at each point in space where
the electric field is NOT zero, the electric field vector is perpendicular to the
equipotential at that point.
• The electric field is strongest where the equipotentials are close together; the electric
field is weaker where the equipotentials are farther apart.
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CP 3 It takes 3.0 µ J of work to move a 15 nC charge from
point A to point B. It takes 5.0 µ J of work to move the
same charge from C to B. What is the potential difference
VC VA?
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CP 7 A proton has been accelerated
from rest through a potential difference
of 1000 V. Calculate its kinetic energy
in (a) electron volts, and (b) joules. (c.)
Calculate its final speed.
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CP 46 What is the potential difference
V34 in the figure?
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CP 48 At a distance r from a point charge, the electric
potential is 3000 V and the magnitude of the electric field
is 2.0 × 105 V/m. (a) Calculate the distance r. (b) Calculate
the electric potential and the magnitude of the electric
field at a distance r/2 from the point charge.
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CP 52 A +3.0 nC charge is at x = 0 cm and a 1.0 nC charge
is at x = 4 cm. At which point or points along the x-axis is
the electric potential zero?
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A charge of 10 nC is placed on a metal sphere that has a radius of
5 cm. Calculate the electric potential at the following distances
from the centre of the sphere: (a) 10 cm (b) 2 cm (c.) 3 cm (d) 5
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cm.
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CP 56 A glass bead with a diameter of 2.0 mm is positively
charged. The potential difference between a point 2.0 mm
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charged. The potential difference between a point 2.0 mm
from the surface of the bead and a point 4.0 mm from the
surface of the bead is 500 V. What is the charge on the bead?
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CP 30 A switch that connects a battery to a 10 µF capacitor is
closed. Several seconds later the capacitor plates are charged
to ±30 µC. What is the battery voltage?
CP 32 Two electrodes connected to a 9.0 V battery are
charged to ±45 nC. What is the capacitance of the electrodes?
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CP 35 A science-fair radio uses a homemade capacitor made of
two 35 cm × 35 cm sheets of aluminum foil separated by a 0.25
mm-thick sheet of paper. What is the capacitance? (Note that
the dielectric constant for paper is 3.0.)
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CP 67 A proton is released from rest at the positive plate of a
parallel-plate capacitor. It crosses the capacitor and reaches
the negative plate with a speed of 50,000 m/s. What will be
the proton's final speed if the experiment is repeated with
double the amount of charge on each capacitor plate?
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CP 80 The dielectric in a capacitor serves two purposes. It
increases the capacitance, compared to an otherwise identical
capacitor with an air gap, and it increases the maximum
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capacitor with an air gap, and it increases the maximum
potential difference the capacitor can support. If the electric
field in a material is sufficiently strong, the material will
suddenly become able to conduct, creating a spark. The critical
field strength, at which breakdown occurs, is 3.0 MV/m for air,
but 60 MV/m for Teflon.
(a) A parallel-plate capacitor consists of two square plates, 15
cm on a side, spaced 0.50 mm apart with only air between them.
What is the maximum energy that can be stored by the
capacitor?
(b) What is the maximum energy that can be stored if the plates
are separated by a 0.50 mm thick Teflon sheet.
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CP 81 The flash unit in a camera uses a special circuit to "step
up" the 3.0 V from the batteries to 300 V, which charges a
capacitor. The capacitor is then discharged through a flash bulb.
The discharge takes 10 µs, and the average power dissipated in
the flash bulb is 105 W. What is the capacitance of the capacitor?
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Key Concepts
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electric potential and electric potential energy
equipotential surfaces and their properties
relation between electric field and electric potential
parallel-plate capacitors
electric potential inside a conductor at equilibrium
how a dielectric changes the properties of a capacitor
energy stored in a capacitor
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CP 21 In the figure, the electric potential at point A
is 300 V. Determine the potential at point B, which is 5.0
cm to the right of A.
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CP 23 Determine the magnitude and direction of
the electric field at the dot in the figure.
CP 37 Two 2.0-cm-diameter electrodes with a 0.10-mmthick sheet of Teflon between them are attached to a 9.0 V
battery. Without disconnecting the battery, the Teflon is
removed. Determine the charge, potential difference, and
electric field (a) before and (b) after the Teflon is removed.
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CP 55 A 10.0 nC point charge and a +20.0 nC point
charge are 15.0 cm apart on the x-axis. (a) Determine the
electric potential at the point on the x-axis where the
electric field is zero. (b) Determine the magnitude and
direction of the electric field at the point on the x-axis,
between the charges, where the electric potential is zero.
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CP 10 A proton with initial speed 800 000 m/s is brought to
rest by an electric field. (a) Did the proton move into a region
of higher potential or lower potential? (b) Determine the
potential difference that stopped the proton. (c.) Determine
the initial kinetic energy of the proton in electron volts.
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