# 19.1 Electric potential energy: potential difference  (Page 3/10)

 Page 3 / 10

Note that the energies calculated in the previous example are absolute values. The change in potential energy for the battery is negative, since it loses energy. These batteries, like many electrical systems, actually move negative charge—electrons in particular. The batteries repel electrons from their negative terminals (A) through whatever circuitry is involved and attract them to their positive terminals (B) as shown in [link] . The change in potential is $\Delta V={V}_{\text{B}}{\mathrm{–V}}_{\text{A}}=\text{+12 V}$ and the charge $q$ is negative, so that $\text{ΔPE}=q\Delta V$ is negative, meaning the potential energy of the battery has decreased when $q$ has moved from A to B.

## How many electrons move through a headlight each second?

When a 12.0 V car battery runs a single 30.0 W headlight, how many electrons pass through it each second?

Strategy

To find the number of electrons, we must first find the charge that moved in 1.00 s. The charge moved is related to voltage and energy through the equation $\text{ΔPE}=q\Delta V$ . A 30.0 W lamp uses 30.0 joules per second. Since the battery loses energy, we have $\text{ΔPE}=\text{–30.0 J}$ and, since the electrons are going from the negative terminal to the positive, we see that $\Delta V=\text{+12.0 V}$ .

Solution

To find the charge $q$ moved, we solve the equation $\text{ΔPE}=q\Delta V$ :

$q=\frac{\text{ΔPE}}{\Delta V}\text{.}$

Entering the values for $\text{Δ}\text{PE}$ and $\text{Δ}V$ , we get

$q=\frac{\text{–30.0 J}}{\text{+12.0 V}}=\frac{\text{–30.0 J}}{\text{+12.0 J/C}}=–2.50 C.$

The number of electrons ${\text{n}}_{\text{e}}$ is the total charge divided by the charge per electron. That is,

${\text{n}}_{\text{e}}=\frac{–2.50 C}{–1.60×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}{\text{C/e}}^{–}}=1.56×{\text{10}}^{\text{19}}\phantom{\rule{0.25em}{0ex}}\text{electrons.}$

Discussion

This is a very large number. It is no wonder that we do not ordinarily observe individual electrons with so many being present in ordinary systems. In fact, electricity had been in use for many decades before it was determined that the moving charges in many circumstances were negative. Positive charge moving in the opposite direction of negative charge often produces identical effects; this makes it difficult to determine which is moving or whether both are moving.

## The electron volt

The energy per electron is very small in macroscopic situations like that in the previous example—a tiny fraction of a joule. But on a submicroscopic scale, such energy per particle (electron, proton, or ion) can be of great importance. For example, even a tiny fraction of a joule can be great enough for these particles to destroy organic molecules and harm living tissue. The particle may do its damage by direct collision, or it may create harmful x rays, which can also inflict damage. It is useful to have an energy unit related to submicroscopic effects. [link] shows a situation related to the definition of such an energy unit. An electron is accelerated between two charged metal plates as it might be in an old-model television tube or oscilloscope. The electron is given kinetic energy that is later converted to another form—light in the television tube, for example. (Note that downhill for the electron is uphill for a positive charge.) Since energy is related to voltage by $\text{ΔPE}=q\Delta V,$ we can think of the joule as a coulomb-volt.

the meaning of phrase in physics
is the meaning of phrase in physics
Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
how does a model differ from a theory
what is vector quantity
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
what's electromagnetic induction
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
Lukman
wow great
Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
yes it was an assignment question "^"represent raise to power pls
Gabriel
Gabriel
An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
no ideas
Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
calculate the force due to surface tension required to support a column liquid in a capillary tube 5mm. If the capillary tube is dipped into a beaker of water
find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
method of polarization
Ajayi
What is atomic number?
The number of protons in the nucleus of an atom
Deborah
type of thermodynamics
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm