Download Circular Motion HW-1

AP Physics-1
Electrostatics HW-3 (“Energy & Potential”):
due______________
Read text Chapter 21 (pages 675 – 694 only)
Conceptual Questions
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In some region of space the electric potential has a positive constant value. What can be said about the electric
field in this region of space?
An electron is released from rest in a region of space with a nonzero electric field. As the electron moves, does
the electric potential energy of the system increase or decrease? Explain.
An electron is released from rest in a region of space with a nonzero electric field. As the electron moves, does it
experience an increasing or decreasing electric potential? Explain.
A proton is released from rest in a region of space with a nonzero electric field. As the proton moves, does the
electric potential energy of the system increase or decrease? Explain.
A proton is released from rest in a region of space with a nonzero electric field. As the proton moves does it
experience an increasing or decreasing electric potential? Explain.
Two like charges a distance r apart have a positive electric potential energy. Conversely, two unlike charges a
distance r apart have a negative electric potential energy. Explain the physical significance of these
observations.
In the Bohr model of the hydrogen atom, a proton and an electron are separated by a constant distance r. Would
the electrical potential energy of this system increase, decrease, or stay the same if (a) the electron were replaced
with a proton or (b) the proton were replaced with an electron? Explain.
In Figure 1, it is given that q1  Q. What value must q2 have if the electric potential at point 1 is to be zero?
With this value for q2 , what is the sign of the potential at point 2? Explain.
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The charge q1 in Figure 1 has the value Q. What value must q2 have if the electric potential at point 2 is to be
zero? With this value for q2 , what is the sign of the potential at point 1? Explain.
It is given that the electric potential is zero at the center of the square in Figure 1. If q1  Q, what is the value
of the charge q2 ? What is the sign of the potential at point 1? At point 2? Explain.
Figure 1
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Figure 2
If the electric field is zero in some region of space is the electric potential zero there as well? Explain.
How much work is required to move a charge from one location on an equipotential to another point on the
same equipotential?
Sketch a slice of the equipotential surface that goes through point 1 in Figure 2.
Repeat for point 2 and for point 3.
Imagine sketching a large number of equipotential surfaces in Figure 2. Would the spacing between the
equipotentials at point 2 be greater than or less than the spacing at point 1? Explain.
Is the electric potential at point 1 in Figure 2 greater than or less than the electric potential at point 3? Explain.
Explain why equipotentials are always perpendicular to the electric field.
It is known that the electric potential is constant on a given two-dimensional surface. What can be said about the
electric field on this surface?
Two charges are at locations that have the same value of the electric potential. Is the electric potential energy the
same for these charges?
Problems
Electric Potential Energy and the Electric Potential
1. A uniform electric field of magnitude 41
.  105 N / C points in the positive x direction. Find the change in
electric potential energy of a 4.5 - C charge as it moves from the origin to the points (a) (0, 6.0 m);
(b) (6.0 m, 0); and (c) (6.0 m, 6.0 m).
2. When an ion accelerates through a potential difference of 2850 V its electric potential energy decreases by
137
.  1015 J. What is the charge on the ion?
3. A uniform electric field with a magnitude of 1200 N/C points in the negative x direction, as shown in Figure 3.
(a) What is the difference in electric potential, V  VB  VA , between points A and B? (b) What is the
difference in electric potential, V  VB  VC , between points B and C? (c) What is the difference in electric
potential, V  VC  VA , between points C and A? (d) From the information given in this problem, is it
possible to determine the value of the electric potential at point A? If so, determine VA ; if not, explain why.
Figure 3
Figure 4
Energy Conservation
4. The electrons in a TV picture tube are accelerated from rest through a potential difference of 25 kV. What is the
speed of the electrons after they have been accelerated by this potential difference?
(me = 9.11 x 10-31 kg, qe = -1.602 x 10-19 C)
5. Find the potential difference required to accelerate protons from rest to 10% of the speed of light. (At this point,
relativistic effects start to become significant.) (mp = 1.67 x 10-27 kg, qp = +1.602 x 10-19 C)
6. A particle with a mass of 3.5 grams and a charge of 0.045 C is released from rest at point A in Figure 3.
(a) In which direction will this charge move?
(b) What speed will it have after moving through a distance of 5.0 cm?
The Electric Potential of Point Charges
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7. The electric potential 1.5 m from a point charge q is 2.8  10 V. What is the value of q?
8. Figure 4 shows three charges at the corners of a rectangle. (a) How much work must be done to move the
2.7 - C charge to infinity? (b) Suppose, instead, that we move the 61
. - C charge to infinity. Is the work
required in this case greater than, less than, or the same as when we moved the 2.7 - C charge to infinity?
Explain. (c) Calculate the work needed to move the 61
. - C charge to infinity.
9. How much work must be done to move the three charges in Figure 4 infinitely far from one another?
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Figure 5
Answers available online as extension of this file. 
In Figure 5, a 12
. - C charge and a 12
. - C charge
are placed at (0.50 m, 0) and (0.50 m, 0), respectively.
(a) At which of the points A, B, C, or D is the electric
potential smallest in value? At which of these points
does it have its greatest value? Explain. (b) Calculate
the electric potential at points A, B, C, and D.
A point charge Q  871
. C is held fixed at the origin.
A second point charge, with mass m  0.0526 kg and
charge q  2.37 C, is placed at the location
(0.323 m, 0). (a) Find the electric potential energy of this
system of charges. (b) If the second charge is released
from rest, what is its speed when it reaches the point
(0.121 m, 0)
Answers
(a) 0
(b) 11 J (c) 11 J
q = 4.81 x 10 19 C = 3.00e (the ion has 3 extra electrons)
(a) 0
(b) 48 V (c) 48V
(d) No, (Explain why we’d need to know the specific charge distribution.)
v = 9.4 x 107 m/s (note that relativistic effects are being ignored)
V = 4.69 MV
(a) Negative x-direction…explain (b) v = 3.9 cm/s
q = 4.7 C
(a) Won charge = +0.86 J
(b) The 6.1 C charge is repelled by the 3.3 C charge more than it is attracted by the 2.7 C charge. The
work required will be negative, which is less than the work required in part (a).
(c) Won charge = 0.54 J
9. Won charges = 0.269 J
10. (a) Explain.
(b) VA = 0, VB = VD = 12 kV,
VC = 14 kV
11. (a) U = 5.75 J
(b) v = 19.1 m/s
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