When capacitor plates are separated, the capacitor's electrostatic energy either increases or decreases, depending upon whether the charge or the voltage is held constant. For the constant-voltage case, an interesting puzzle can be posed to students: How is it possible that an external agent does positive work on the capacitor while at the same time the capacitor's stored energy decreases? An energy flow diagram, as suggested by Art Hobson's TPT article,1 helps to visualize the movements of energy among different parts of the system. What Richard Feynman calls a “surprising factor of one-half” in the expression for the force between capacitor plates confronts students with an additional puzzle to decipher.2
REFERENCES
1.
A.
Hobson
, “Energy flow diagrams for teaching physics concepts
,” Phys. Teach.
42
, 113
–117
(Feb. 2004
).2.
R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II (Addison-Wesley, Reading, MA, 1964), pp. 82–84.
3.
R. J.
Harwood
and D. E.
Kinkaid
, “Use of a mettler balance and parallel plate capacitor to measure the permittivity of free space
,” Am. J. Phys.
43
, 924
(Oct. 1975
).4.
F. N.
Yan
and H. K.
Wong
, “Force between the plates of a parallel-plate capacitor
,” Am. J. Phys.
61
, 1153
(Dec. 1993
).5.
Another way of looking at the situation is to imagine momentarily disconnecting the battery while the capacitor's separation increases from x to The potential difference across the capacitor plates will rise to Now reconnect the battery, and the mismatch in voltages will drive an infinitesimal current “uphill” through the battery. With each iteration of this procedure, the capacitor's charge, and hence electric field E, decays.
This content is only available via PDF.
© 2005 American Association of Physics Teachers.
2005
American Association of Physics Teachers
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
