Simple Nature - Light and Matter

d/Example 4.

Force depends only on position. Since the charge distri-

bution is not changing, the total electrical force on a charged

particle depends only on its own charge and on its location.

If another charged particle of the same type visits the same

location later on, it will feel exactly the same force.

The second observation tells us that there is nothing all that

different about the experience of one charged particle as compared

to another’s. If we single out one particle to pay attention to, and

figure out the amount of work done on it by electrical forces as it

goes from point A to point B along a certain path, then this is

the same amount of work that will be done on any other charged

particles of the same type as it follows the same path. For the sake of

visualization, let’s think about the path that starts at one terminal

of the battery, goes through the light bulb’s filament, and ends at

the other terminal. When an object experiences a force that depends

only on its position (and when certain other, technical conditions

are satisfied), we can define an electrical energy associated with the

position of that object. The amount of work done on the particle by

electrical forces as it moves from A to B equals the drop in electrical

energy between A and B. This electrical energy is what is being

converted into other forms of energy such as heat and light. We

therefore define ∆V in general as electrical energy per unit charge:

The ∆V between two points in space is defined as

∆V = ∆Uelec/q,

where ∆Uelecis the change in the electrical energy of a particle with

chargeqas it moves from the initial point to the final point. In this

context, where we think of the voltage as being a scalar function

that is defined everywhere in space, it is more common in formal

writing to refer to it as the electricalpotential.

The amount of power dissipated (i.e., rate at which energy is

transformed by the flow of electricity) is then given by the equation

P=I∆V.

Energy stored in a battery example 4

.The 1.2 V rechargeable battery in figure d is labeled 1800 milliamp-

hours. What is the maximum amount of energy the battery can

store?

.An ampere-hour is a unit of current multiplied by a unit of time.

Current is charge per unit time, so an ampere-hour is in fact a

funny unit ofcharge:

(1 A)(1 hour) = (1 C/s)(3600 s)

= 3600 C

536 Chapter 9 Circuits