29.11 You measure the electric field be- tween the plates of a 5 nC capacitor to be 2000 N C-¹. If the charge on this capaci- tor is 2 µC, how far apart are the plates? f
29.11 You measure the electric field be- tween the plates of a 5 nC capacitor to be 2000 N C-¹. If the charge on this capaci- tor is 2 µC, how far apart are the plates? f
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Need help with question 11 and 14 please, thank you.
Transcribed Image Text:29.4 A capacitor stores charge ±Q on
each plate when there is a potential dif-
ference of V between the plates.
What is the capacitance given the follow-
ing pairs of values?
(a) Q=1.0 C, V = 1.0 V
(b) Q = 5.0 μC, V = 12.0 V
(c)
Q = 0.75 mC, V = 15.0 kV
Q = 90 C, V = 15.0 kV
(d)
(e) Q = 6.6 C, V = 3.3 V
(f) Q = 20 nC, V = 60 V
(g) Q = 5.4 mC, V = 8.2 V
(h) Q = 12 µC, V = 2 mV
29.5 What is the magnitude of the elec-
tric field between the plates of each of the
parallel plate capacitors below?
(b) A capacitor with an area of 50 m²,
the plates separated by a 1.0 mm
layer of a dielectric with & = 120,
with each plate connected to the op-
posite terminal of a 9 V battery?
(c) A capacitor of capacitance 9.0 μF
storing 0.2 mC of charge and where
the plates are separated by 2.0 mm.
(d) A capacitor which required
3.2 x 10-16 J of energy to to add
the last electron and in which the
plates are separated by 0.2 mm.
(e) A capacitor of capacitance 1.2 µC
storing 10 µJ of energy and with
plates of area 2.0 m² separated by a
vacuum.
29.6 A 9V battery is connected to a ca-
pacitor which subsequently has a magni-
tude of 0.5 µC of charge on each plate,
with the charge on each plate having an
opposite sign. What is the capacitance of
this capacitor?
0.5 m x 0.2 m and the shelves are 0.3 m
apart. (assume the shelves are electri-
cally insulated from each other and any
other objects)
29.7 You have some metal shelving
with two shelves, each of which measures
(a) What is the capacitance of your
shelves?
(b) How much charge would they hold
if you connected each terminal of
the shelves to a 1.25 V battery?
29.8
You wish to construct a capaci-
tor which has a capacitance of 1 F. You
intend to construct your capacitor using
two parallel sheets of tinfoil held 1 mm
apart by placing plastic wrap between
them (the plastic wrap fills the space be-
tween the tinfoil). Both tinfoil and plastic
wrap come in rolls which measure 30 cm
by 10 m. The relative permittivity of the
plastic wrap is &₁ = 2.9.
(a) A capacitor with an area of 1.5 m², (a) How many rolls of tinfoil and plastic (c)
the plates separated by a 1.0 mm air
gap, with each plate connected to
wrap would you need? Is your plan
feasible?
(d)
the opposite terminal of a 9 V bat-
tery?
(b)
How much charge could you store
on this capacitor if you connect it to
a standard 9 V battery?
29.9 A large industrial capacitor with an
air gap between the plates stores 140 kJ of
energy at a potential difference of 1200 V.
A dielectric is inserted into the space be-
tween the plates of this capacitor and it
can now store 11200 kJ of energy at 600 V.
What is the relative permittivity of the di-
electric inserted between the plates of the
capacitor?
29.10 A particular capacitor stores 1 J of
energy when charged to a potential differ-
ence of 12 V.
(a)
(b)
What is the capacitance of this ca-
pacitor?
What is the charge stored on this ca-
pacitor?
29.12 You place books in the shelving
described in Problem 29.7. The relative
permittivity of paper is 2.4. How much
charge does each of your bookshelves
hold when connected to the same battery
as before?
29.11 You measure the electric field be-
tween the plates of a 5 nC capacitor to be
2000 N C-¹. If the charge on this capaci-
tor is 2 µC, how far apart are the plates?
29.13 You have a sheet of paper which
measures 15 cm x 20 cm and a piece of
nylon sheeting which has the same di-
mensions. You charge these objects by
rubbing them together and when you
separate them and hold them parallel to
there is an electric field of magnitude
each other and 1 cm apart you find that
1500 V m¹ between them (you can as-
sume that & = 1 for air).
(a)
(b)
(f)
What : the potential difference be-
tween the paper and nylon sheets?
What is the capacitance of these
sheets in this position?
(g)
What is the magnitude of the charge
on each sheet?
The two sheets are now moved further
apart to a separation of 5 cm.
(e)
How much electrical energy is
stored in the sheets?
What is the capacitance of the
sheets now?
What is the potential difference be-
tween the sheets now?
What is the magnitude of the elec-
tric field between the sheets now?
(h) How much electrical energy is
stored in the sheets now?
29.14
Nerve cells maintain a charge
separation across their cell membrane.
The cell membrane of a particular cell is
10 nm thick and the cell can be modeled
as a cylinder with a diameter of 12 µm
and a length of 80 µm. If the potential
difference across the cell membrane is
90 mV, what is the charge stored on the
cell? (you can assume that &, = 1 and
you should use the total surface area of
the cell in the calculation)
29.15 How much energy is stored in the
form of charge separation in the cell in
Problem 29.14?
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