# 8.5 Molecular model of a dielectric  (Page 5/13)

 Page 5 / 13

## Key equations

 Capacitance $C=\frac{Q}{V}$ Capacitance of a parallel-plate capacitor $C={\epsilon }_{0}\frac{A}{d}$ Capacitance of a vacuum spherical capacitor $C=4\pi {\epsilon }_{0}\frac{{R}_{1}{R}_{2}}{{R}_{2}-{R}_{1}}$ Capacitance of a vacuum cylindrical capacitor $C=\frac{2\pi {\epsilon }_{0}l}{\text{ln}\left({R}_{2}\text{/}{R}_{1}\right)}$ Capacitance of a series combination $\frac{1}{{C}_{\text{S}}}=\frac{1}{{C}_{1}}+\frac{1}{{C}_{2}}+\frac{1}{{C}_{3}}+\text{⋯}$ Capacitance of a parallel combination ${C}_{\text{P}}={C}_{1}+{C}_{2}+{C}_{3}+\text{⋯}$ Energy density ${u}_{E}=\frac{1}{2}{\epsilon }_{0}{E}^{2}$ Energy stored in a capacitor ${U}_{C}=\frac{1}{2}{V}^{2}C=\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\frac{{Q}^{2}}{C}=\frac{1}{2}QV$ Capacitance of a capacitor with dielectric $C=\kappa {C}_{0}$ Energy stored in an isolated capacitor with dielectric $U=\frac{1}{\kappa }{U}_{0}$ Dielectric constant $\kappa =\frac{{E}_{0}}{E}$ Induced electrical field in a dielectric ${\stackrel{\to }{E}}_{\text{i}}=\left(\frac{1}{\kappa }-1\right){\stackrel{\to }{E}}_{0}$

## 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.

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

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

Water is a good solvent.

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.

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.

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 .)

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

answers may vary

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.

## 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?

For a Teflon™-filled, parallel-plate capacitor, the area of the plate is $50.0\phantom{\rule{0.2em}{0ex}}{\text{cm}}^{2}$ 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

Find the capacitance of a parallel-plate capacitor having plates with a surface area of $5.00\phantom{\rule{0.2em}{0ex}}{m}^{2}$ and separated by 0.100 mm of Teflon™.

(a) What is the capacitance of a parallel-plate capacitor with plates of area $1.50\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ 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. $4.4\phantom{\rule{0.2em}{0ex}}\text{μ}\text{F}$ ; b. $4.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{-5}}\phantom{\rule{0.2em}{0ex}}\text{C}$

#### Questions & Answers

Maxwell's stress tensor is
Ami Reply
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Jaffar
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply

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