19.P.66 Insert plastic into a capacitor
(a) In the final state of static equilibrium there is no E inside the resistor and wires, so the round-trip potential
difference is . Therefore .
(b) Field argument: Polarized molecules in plastic contribute a field just outside the capacitor that is in the
opposite direction to the fringe field of the plates, so field due to capacitor(plates and plastic) is reduced.
The net field had been zero and is now nonzero due to the reduction in the field contributed by the capacitor,
so current runs. The current will run until the fringe field of the capacitor again is large enough to cancel the
field of all other charges.
Potential argument: E inside gap is reduced by a factor of 1/K, so is reduced to
. That means that the loop rule requires a potential difference across the resistor, and hence
current will run until the potential difference across the capacitor is again equal to emf.
(c) E inside gap is reduced by a factor of 1/K, so is reduced to . The loop rule
becomes , and the initial current is
(d) The effective capacitance has changed:
+emf()ΔVcap
–()+0=QCΔVcap Cemf⋅==
ΔVcap Es=
ΔVcap emf K⁄=
ΔVcap Es=ΔVcap emf K⁄=
+emf()emf K⁄–()RI–()++0=
Iemf
R
----------11
K
---–
⎝⎠
⎛⎞
=
Cnew Q
ΔV
------- Q
Es
----- Q
QA⁄()
Kε0
----------------
⎝⎠
⎛⎞
---------------------- Kε0A
s
---------
⎝⎠
⎛⎞KC=== = =
Qnew Cnew emf()KC emf()==
