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Key equations

Capacitance C = Q V
Capacitance of a parallel-plate capacitor C = ε 0 A d
Capacitance of a vacuum spherical capacitor C = 4 π ε 0 R 1 R 2 R 2 R 1
Capacitance of a vacuum cylindrical capacitor C = 2 π ε 0 l ln ( R 2 / R 1 )
Capacitance of a series combination 1 C S = 1 C 1 + 1 C 2 + 1 C 3 +
Capacitance of a parallel combination C P = C 1 + C 2 + C 3 +
Energy density u E = 1 2 ε 0 E 2
Energy stored in a capacitor U C = 1 2 V 2 C = 1 2 Q 2 C = 1 2 Q V
Capacitance of a capacitor with dielectric C = κ C 0
Energy stored in an isolated capacitor with
dielectric
U = 1 κ U 0
Dielectric constant κ = E 0 E
Induced electrical field in a dielectric E i = ( 1 κ 1 ) E 0

Conceptual questions

Distinguish between dielectric strength and dielectric constant.

Dielectric strength is a critical value of an electrical field above which an insulator starts to conduct; a dielectric constant is the ratio of the electrical field in vacuum to the net electrical field in a material.

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Water is a good solvent because it has a high dielectric constant. Explain.

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Water has a high dielectric constant. Explain why it is then not used as a dielectric material in capacitors.

Water is a good solvent.

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Elaborate on why molecules in a dielectric material experience net forces on them in a non-uniform electrical field but not in a uniform field.

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Explain why the dielectric constant of a substance containing permanent molecular electric dipoles decreases with increasing temperature.

When energy of thermal motion is large (high temperature), an electrical field must be large too in order to keep electric dipoles aligned with it.

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Give a reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. How does a dielectric material also allow a greater voltage to be applied to a capacitor? (The dielectric thus increases C and permits a greater V .)

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Elaborate on the way in which the polar character of water molecules helps to explain water’s relatively large dielectric constant.

answers may vary

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Sparks will occur between the plates of an air-filled capacitor at a lower voltage when the air is humid than when it is dry. Discuss why, considering the polar character of water molecules.

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Problems

Two flat plates containing equal and opposite charges are separated by material 4.0 mm thick with a dielectric constant of 5.0. If the electrical field in the dielectric is 1.5 MV/m, what are (a) the charge density on the capacitor plates, and (b) the induced charge density on the surfaces of the dielectric?

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For a Teflon™-filled, parallel-plate capacitor, the area of the plate is 50.0 cm 2 and the spacing between the plates is 0.50 mm. If the capacitor is connected to a 200-V battery, find (a) the free charge on the capacitor plates, (b) the electrical field in the dielectric, and (c) the induced charge on the dielectric surfaces.

a. 37 nC; b. 0.4 MV/m; c. 19 nC

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Find the capacitance of a parallel-plate capacitor having plates with a surface area of 5.00 m 2 and separated by 0.100 mm of Teflon™.

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(a) What is the capacitance of a parallel-plate capacitor with plates of area 1.50 m 2 that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?

a. 4.4 μ F ; b. 4.0 × 10 -5 C

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Questions & Answers

what is atom
Alh Reply
need help to learn concept of physics
chander Reply
Explain?
The
pls what is gold leaf
Ameenu
is an electric charge brought near to, or on the top conducting plate causes the leaves to stand apart from each other at an angle and the like electric charge either induced in, or transferred to each leaf causes them to repel each other
Fa
explain
Evans
what is kinetic energy
Paul Reply
it is the energy possessed by a body in motion
Senior
what is ferromagnetic materials
What is electric charge
Paul Reply
the thing which is carried by a subatomic particle and by virtue of which a matter feels a force in an electro magnetic fields is Charge....it is basic property of matter and it occurs in a discrete natural units which can neither be generated nor be destroyed....
ashwani
what is meant by damped oscillation
chukwujekwu Reply
how to calculate the field at point P of two charges
Jonah Reply
As shown below, if the heat absorbed by the gas along AB is 400 J, determine the quantities of heat absorbed along ADCB.
Bangtan Reply
I don't see any diagram
PRINCE
Ho.. Sorry I made a mistake so I'll try it again later.
ENDY
why are humans not sensitive to temperature
frances Reply
if I want to convert inch to millimeter what are the formula?
Harun Reply
applications of electromagnetic spectrum
James Reply
Figure, shows a pencil partially immersed in a cup of water. Why does the pencil appear to be ?bent
Motion
Abdulrahman
refraction of light.
chigozie
what is heat capacity
Sessy Reply
joule
Abdikadir
defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin
Abdikadir
formula of acid hydride
Suman Reply
what is mass
Exildah Reply
mass is the amount of staff made up an object
Van
physic is anatural science that deals about scleral
Abdilahi
mass is accelaration divided force
Abdilahi
mass is force divided by acceleration
Van
Is the amout of matter contain in a body
El-shaddai
mass is the quantitative measure of inertia
chukwujekwu
Newton's laws of motion
Nyanachiek
Practice Key Terms 5

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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