# 9.2 Model of conduction in metals  (Page 5/7)

 Page 5 / 7

Check Your Understanding The current density is proportional to the current and inversely proportional to the area. If the current density in a conducting wire increases, what would happen to the drift velocity of the charges in the wire?

The current density in a conducting wire increases due to an increase in current. The drift velocity is inversely proportional to the current $\left({v}_{d}=\frac{nqA}{I}\right)$ , so the drift velocity would decrease.

What is the significance of the current density? The current density is proportional to the current, and the current is the number of charges that pass through a cross-sectional area per second. The charges move through the conductor, accelerated by the electric force provided by the electrical field. The electrical field is created when a voltage is applied across the conductor. In Ohm’s Law , we will use this relationship between the current density and the electrical field to examine the relationship between the current through a conductor and the voltage applied.

## Summary

• The current through a conductor depends mainly on the motion of free electrons.
• When an electrical field is applied to a conductor, the free electrons in a conductor do not move through a conductor at a constant speed and direction; instead, the motion is almost random due to collisions with atoms and other free electrons.
• Even though the electrons move in a nearly random fashion, when an electrical field is applied to the conductor, the overall velocity of the electrons can be defined in terms of a drift velocity.
• The current density is a vector quantity defined as the current through an infinitesimal area divided by the area.
• The current can be found from the current density, $I=\underset{\text{area}}{\iint }\stackrel{\to }{J}·d\stackrel{\to }{A}$ .
• An incandescent light bulb is a filament of wire enclosed in a glass bulb that is partially evacuated. Current runs through the filament, where the electrical energy is converted to light and heat.

## Conceptual questions

Incandescent light bulbs are being replaced with more efficient LED and CFL light bulbs. Is there any obvious evidence that incandescent light bulbs might not be that energy efficient? Is energy converted into anything but visible light?

It was stated that the motion of an electron appears nearly random when an electrical field is applied to the conductor. What makes the motion nearly random and differentiates it from the random motion of molecules in a gas?

Even though the electrons collide with atoms and other electrons in the wire, they travel from the negative terminal to the positive terminal, so they drift in one direction. Gas molecules travel in completely random directions.

Electric circuits are sometimes explained using a conceptual model of water flowing through a pipe. In this conceptual model, the voltage source is represented as a pump that pumps water through pipes and the pipes connect components in the circuit. Is a conceptual model of water flowing through a pipe an adequate representation of the circuit? How are electrons and wires similar to water molecules and pipes? How are they different?

An incandescent light bulb is partially evacuated. Why do you suppose that is?

In the early years of light bulbs, the bulbs are partially evacuated to reduce the amount of heat conducted through the air to the glass envelope. Dissipating the heat would cool the filament, increasing the amount of energy needed to produce light from the filament. It also protects the glass from the heat produced from the hot filament. If the glass heats, it expands, and as it cools, it contacts. This expansion and contraction could cause the glass to become brittle and crack, reducing the life of the bulbs. Many bulbs are now partially filled with an inert gas. It is also useful to remove the oxygen to reduce the possibility of the filament actually burning. When the original filaments were replaced with more efficient tungsten filaments, atoms from the tungsten would evaporate off the filament at such high temperatures. The atoms collide with the atoms of the inert gas and land back on the filament.

## Problems

An aluminum wire 1.628 mm in diameter (14-gauge) carries a current of 3.00 amps. (a) What is the absolute value of the charge density in the wire? (b) What is the drift velocity of the electrons? (c) What would be the drift velocity if the same gauge copper were used instead of aluminum? The density of copper is $8.96{\phantom{\rule{0.2em}{0ex}}\text{g/cm}}^{3}$ and the density of aluminum is $2.70{\phantom{\rule{0.2em}{0ex}}\text{g/cm}}^{3}$ . The molar mass of aluminum is 26.98 g/mol and the molar mass of copper is 63.5 g/mol. Assume each atom of metal contributes one free electron.

The current of an electron beam has a measured current of $I=50.00\phantom{\rule{0.2em}{0ex}}\mu \text{A}$ with a radius of $1.00\phantom{\rule{0.2em}{0ex}}{\text{mm}}^{2}$ . What is the magnitude of the current density of the beam?

$|J|=15.92{\phantom{\rule{0.2em}{0ex}}\text{A/m}}^{2}$

A high-energy proton accelerator produces a proton beam with a radius of $r=0.90\phantom{\rule{0.2em}{0ex}}\text{mm}$ . The beam current is $I=9.00\phantom{\rule{0.2em}{0ex}}\mu \text{A}$ and is constant. The charge density of the beam is $n=6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{11}$ protons per cubic meter. (a) What is the current density of the beam? (b) What is the drift velocity of the beam? (c) How much time does it take for $1.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{10}$ protons to be emitted by the accelerator?

Consider a wire of a circular cross-section with a radius of $R=3.00\phantom{\rule{0.2em}{0ex}}\text{mm}$ . The magnitude of the current density is modeled as $J=c{r}^{2}=5.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\frac{\text{A}}{{\text{m}}^{4}}{r}^{2}$ . What is the current through the inner section of the wire from the center to $r=0.5R$ ?

$\begin{array}{cc}\hfill I& =40\phantom{\rule{0.2em}{0ex}}\text{mA}\hfill \end{array}$

The current of an electron beam has a measured current of $I=50.00\phantom{\rule{0.2em}{0ex}}\mu \text{A}$ with a radius of $1.00\phantom{\rule{0.2em}{0ex}}{\text{mm}}^{2}$ . What is the magnitude of the current density of the beam?

The current supplied to an air conditioner unit is 4.00 amps. The air conditioner is wired using a 10-gauge (diameter 2.588 mm) wire. The charge density is $n=8.48\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{28}\frac{\text{electrons}}{{\text{m}}^{3}}$ . Find the magnitude of (a) current density and (b) the drift velocity.

a. $|J|=7.60\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\frac{\text{A}}{{\text{m}}^{2}}$ ; b. ${v}_{\text{d}}=5.60\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\frac{\text{m}}{\text{s}}$

What is dielectric
its a type of medium. generally poor conductors. but their conductivity can be changed
vedanth
you just have to add impurities
vedanth
Thanks
Ssempala
grt
Ssempala
a material which behave as conductor
Shikhar
insulating material, energy level for electron transfer is very high e.g used to increase a magnetic field in a capacitor
What is the difference between specific heat capacity and heat capacity? Give the equations
presentation on power
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Newton's second laws is call with
what is mean by thermodynamics
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
show mathematically that an electron has the greater speed than the proton when they attract each other
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar
what is electrostatics
the study of charge at rest
Gulzar
@Hero; the study of charges at rest is the electrostatics
Sikandar
okay what is electrostatic?
Abd
charge at rest
Nawal
set of character...
Arzoodan
oky
Abd
Gauss law, electric fields, dipoles,...
Antonio
good
Abd
A proton initially at rest falls through a p.d of 25000V. what speed does it gain?
@Minister; use equation v= sq root(2×eV/m)
Sikandar
what is the reaction of heat on magnet
Magnetization decreases with increase in temperature. But in case of diamagnetic substance heat has no role on magnetization.
srikanta
what is a physical significant of electric dipole moment .
A dipole moment it's a mechanical electrical effect used in nature
Antonio
what is the uses of carbon brushes in generator
to minimize heat
constand
at what temperature is the degree Fahrenheit equal to degree Celsius
Celsius and Faharaneith are different, never equal
Antonio
find their liners express of n=a+b/T² ( plot graph n against T)