# 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.

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. $4.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{\text{-5}}\phantom{\rule{0.2em}{0ex}}\text{C}$

The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
what is copper loss
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
Henry
it is the work done in moving a charge to a point from infinity against electric field
what is the weight of the earth in space
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge
please why is the first law of thermodynamics greater than the second
define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
explain the lack of symmetry in the field of the parallel capacitor
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe
does your app come with video lessons?
What is vector
Vector is a quantity having a direction as well as magnitude
Damilare
tell me about charging and discharging of capacitors
a big and a small metal spheres are connected by a wire, which of this has the maximum electric potential on the surface.
3 capacitors 2nf,3nf,4nf are connected in parallel... what is the equivalent capacitance...and what is the potential difference across each capacitor if the EMF is 500v
equivalent capacitance is 9nf nd pd across each capacitor is 500v
santanu
four effect of heat on substances
why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
because you can't fit the boundary conditions.
Jorge
what is the dimensions for VISCOUNSITY (U)
Branda