Electrostatics.ppt

7/27/2019 Electrostatics.ppt

1/13

Electrostatics

Electric charge

Conservation of charge

Insulators & conductors

Charging objects

Static electricity

Coulombs law

Systems of charges


2/13

Electric Charge

Just as most particles have an attribute known as mass, many

possess another attribute called charge. Charge and mass are intrinsicproperties, defining properties that particles possess by their very

nature.

Unlike mass, there are two different kinds of charge: positive and

negative. Particles with a unlike charges attract, while those with like charges

repel.

Most everyday objects are comprised of billions of charged, but

usually there are about the same number of positive charges as

negative, leaving the object as a whole neutral.

A charged object is an object that has an excess of one type of

charge, e.g., more positive than negative. The amount of excess

charge is the charge we assign to that object.


3/13

SI unit of Charge: the Coulomb

Just as we have an SI unit for mass, the kilogram, we have one

for charge as well. Its called the coulomb, and its symbol is C.

Its named after a French physicist, Charles Coulomb, who did

research on charges in the mid and late 1700s.

A coulomb is a fairly large amount of charge, so sometimes

we measure small amounts of charge in C (mircocoloumbs).

An electron has a charge of -1.6

10-19

C. A proton has a charge of +1.6 10-19 C.

In a wire, if one coulomb of charge flows past a point in one

second, we say the current in the wire is one ampere.


4/13

Elementary Charge

Charges come in small, discrete bundles. Another way to say this

is that charge is quantized. This means an object can possesscharge in incremental, rather than continuous, amounts.

Imagine the graph of a linear function buy when you zoom in

very close you see that it really is a step function with very small

steps.

The smallest amount of charge that can be added or removed

from an object is the elementary charge, e = 1.6 10-19 C.

The charge of a proton is +e, an electron -e.The charge of an object, Q, is always a multiple of this

elementary charge: Q = Ne, where N is an integer.

How many excess protons are required for an object to have 1 C

of charge?


5/13

Insulators vs. Conductors A conductoris a material in which excess charge freely flows.

Metals are typically excellent conductors because the valence (outershell) electrons in metal atoms are not confined to any one atom.

Rather, they roam freely about a metal object. Metal are excellent

conductors of electricity (and heat) for this reason.

An insulatoris a material in which excess charge, for the mostpart, resides where it is deposited. That is, once placed, it does not

move. Most nonmetallic material are good insulators. Valence

electrons are much more tightly bound to the atoms and are not free

to roam about. Insulators are useful for studying electrostatics (the

study of charge that can be localized and contained).

Semi-conductors, like silicon used in computer chips, have

electrical conductivity between that of conductors and insulators.


6/13

Charging up Objects

Charging up an object does not mean creating new charges. Chargingimplies either adding electrons to an object, removing electrons from

an object, or separating out positive and negative charges within an

object. This can be accomplish in 3 different ways:

Friction: Rubbing two materials together can rub electrons off of

one and onto the other.

Conduction: Touching an object to a charged object could lead to a

flow of charge between them.

Induction: If a charged object is brought near (but not touching) asecond object, the charged object could attract or repel electrons

(depending on its charge) in the second object. This yields a

separation charge in the second object, an induced charge separation.


7/13

Redistributing Charge on Conducting Spheres

A B

-Q- - -

B

Two neutral spheres, A & B, are placed side by side, touching. A negatively

charged rod is brought near A, which induces a charge separation in the A-B

system. Some of the valence e-s in A migrate to B. When the rod is re-moved and A & B are separated, A is +, B is -, but the system is still neutral.

A

+Q

A is now brought near neutral sphere C, inducing a charge separation on it.

Valence e-s in C migrate toward A, but since C is being touched on the

positive side, e-s from the hand will move into C. Interestingly, C retains a

net negative charge after A and the hand are removed even though nocharged object ever made contact with it.

A

+Q

C C

-


8/13

Static Electricity: Shocks

If you walk around on carpeting in your stocking feet, especially in

the winter when the air is dry, and then touch something metal, you

may feel a shock. As you walk you can become negatively charged

by friction. When you make contact with a metal door knob, you

discharge rapidly into the metal and feel a shock at the point of

contact. A similar effect occurs in the winter when you exit a car: if

you slide out of your seat and touch then touch the car door, youmight feel a shock.

The reason the effect most often occurs in winter is because the air is

typically drier then. Humidity in the air can rather quickly rob excess

charges from a charged body, thereby neutralizing it before a rapid,localized discharge (and resulting shock) can take place.

Care must be taken to prevent static discharges where sensitive

electronics are in use or where volatile substances are stored.


9/13

Coulombs Law

K= 9109 Nm2/C2

Coulomb's Law Detailed ExampleCharges in Motion

F=Kq1q2

r2

There is an inverse square formula, called Coulombs law, for finding

the force on one point charge due to another:

This formula is just like Newtons law of uniform gravitation with charges

replacing masses and K replacing G. It states that the electric force oneach of the point charges is directly proportional to each charge and

inversely proportional to the square of the distance between them. The

easiest way to use the formula to ignore signs when entering charges, since

we already know that like charges repel and opposites attract. K is the

constant of proportionality. Its units serve to reduce all units on the right tonothing but newtons. Forces are equal but opposite.

+ -q1 q2

rF F
http://physics.bu.edu/py106/notes/Coulomb.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wavpart2.htmlhttp://www.colorado.edu/physics/2000/waves_particles/wavpart2.htmlhttp://physics.bu.edu/py106/notes/Coulomb.html


10/13

Electric Force vs. Gravitational Force

K= 9109

Nm2

/C2

FE =

Kq1q2

r2

G = 6.6710-11

Nm2

/kg2

FG =

Gm1m2

r2Gravity is the dominant force when it comes to shaping galaxies and the

like, but notice that K is about 20 orders of magnitude greater than G.

Technically, they cant be directly compared, since they have differentunits. The point is, though, that a whole lot of mass is required to produce

a significant force, but a relatively small amount of charge can overcome

this, explaining how the electric force on a balloon can easily match the

balloons weight. When dealing with high-charge, low-mass objects, such

as protons & electrons, the force of gravity is negligible.


11/13

Electric Force Example

+ +15 m

A proton and an electron are separated by 15 m. They are released from rest.

Our goal is to find the acceleration each undergoes at the instant of release.

1. Find the electric force on each particle.

2. Find the gravitational force on each particle. A protons mass is

1.67 10-27 kg, and an electrons mass is 9.11 10-31 kg.

3. Find the net force on each and round appropriately. Note that the

gravitational force is inconsequential here.

4. Find the acceleration on each particle.

5. Why couldnt we use kinematics to find the time it would take

the particles to collide?

1.02410-18N

4.5110-58N

1.02410-18N

e-: 1.1241012 m/s2, p+: 6.13108 m/s2

r changes, so F changes, so a changes.


12/13

Equilibrium with Several ChargesSeveral equal point charges are to be arranged in a plane so that another point

charge with non-negligible mass can be suspended above the plane. How might this

be done?Arrange the charges in a circle, spaced evenly, and fix them in place.

Place another charge of the same sign above the center of the circle. If placed at

the right distance above the plane, the charge could hover. This arrangement works

because of symmetry. The electric force vectors on the hovering charge are shown.

Each vector is the same magnitude and they lie in a cone. Each vector has a verticalcomponent and a component in the plane. The planar components cancel out, but

the vertical components add to negate

the weight vector. Continued


13/13

Equilibrium with Several Charges (cont.)Note that the charges in the plane are fixed. That is, they are attached somehow in

the plane. They could, for example, be attached to an insulating ring, which is then

set on a table. Regardless, how could the arrangement of charges in the plane be

modified so as to maintain equilibrium of the hovering charge but allow it to hover

at a different height?

If the charges in the plane are arranged in a circle with a large radius, the

electric force vectors would be more horizontal, thereby working together less and

canceling each other more. The hovering charge would lower. Since its weightdoesnt change, it must be closer to the plane in order to increase the forces to

compensate for their partial cancellation. If the charges in the plane were arranged

in a small circle, the vectors would be more vertical, thereby working together

more and canceling each other less. The hovering charge would rise and the vectors

would decrease in magnitude. To maximize the height of the hovering charge, all

the charges in the plane should be brought to a single point. Continued

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