Electrostatics

• Electrical Forces

• Electric Charges– conservation; Coulomb’s Law

• Electrical Conductors and Insulators– semiconductors and superconductors

• Charging

• Electric Field

• Electric Potential

Electrostatics

• Electrostatics is the study of stationary charges

• Electric Force– follows inverse-square law like gravity– Two varieties: attractive and repulsive

• Electric force is produced by electric charge, just as gravitational force is produced by gravitational mass.

Electric Charges

• Assume two types of charges, positive (+) and negative (–).

• Like charges repel (+) ↔ (+) or (–) ↔ (–)• Opposite charges attract (+)––> <––(–)• Protons are positive (+)• Electrons are negative (–)• Neutrons have no net charge.• Every atom has protons and electrons

32.2 Conservation of Charge

• Conservation of Charge

• An object that has unequal numbers of electrons and protons is electrically charged.

• An atom with a net positive charge is a positive ion; it has lost one or more electrons.

• An atom with a net negative charge is a negative ion; it has gained one or more electrons.

• The principle that electrons are neither created nor destroyed but are simply transferred from one material to another is known as conservation of charge.

Law of Conservation of Electric Charge- During any process, the net electric charge of an isolated system remains constant ( is conserved).

Total charge before= Total charge after.

32.3 Coulomb’s Law• q = charge of particle; +q or -q

• Coulomb’s law states that for charged particles or objects that are small compared with the distance between them, the force between the charges varies directly as the product of the charges and inversely as the square of the distance between them.

Coulomb appletElectric filed lines applet

32.3 Coulomb’s Law

221kqF

d

q

• F = kq1q2/d2, where d is the distance between the charged particles

• q1 represents the quantity of charge of one particle and q2 the quantity of charge of the other particle. The SI unit of charge is the coulomb, abbreviated C.

• The proportionality constant k in Coulomb’s law is 9.0 x 109 Nm2/C2.

• 1 electron has a charge of 1.60 x 10-

19 C {either (+) or (-)}.

• Like all other forces, the electrostatic force between two charged objects is measured in Newtons (N).

• -F = attraction and +F = repulsion

32.3 Coulomb’s Law1. Consider a pair of charged particles separated by a distance d. If the distance between the particles is multiplied

by 4, how will the electrostatic force between the particles change?

2. If the charge of each particle tripled and the distance also tripled, how would the electrostatic force between the particles change?

3. If the charge of one particle doubled and the charge of the other particle tripled, how would the electrostatic force between the particles change?

4. If the charge of one particle were reduced to one-half the original charge and the distance between the charges were multiplied by 2, how would the electrostatic force between the particles change?

32.3 Coulomb’s Law

1. Sue rubs two latex balloons against her hair, causing the balloons to become charged negatively with 2.0 x 10 -6 C. She holds them a distance of 0.70 m apart. a) What is the electric force between the two balloons? b) Is it one of attraction or repulsion?

2. Two pieces of puffed rice become equally charged as they are poured out of the box and into Kirk’s cereal bowl. If the force between the puffed rice pieces is 4 x 10-23 N when the pieces are 0.03 m apart, what is the charge on each of the pieces?

Atomic Structure

• Every atom has a positively charged nucleus surrounded by negatively charged electrons.

• Electrons all have same charge and same mass – same for protons.

• Protons have an amount of positive charge equal to the negative charge on electrons, but about 1800 times as much mass.

• Neutrons have almost the same mass a protons, but no net charge.

• Atoms have as many electrons as protons, so have no net charge (normally).

How does the electrical force between the proton and the electron in the hydrogen atom compare to the gravitational force between these two particles. Given: Bohr radius, r = 5.29 x 10-11 m, use the mass of the proton and electron to two decimal places. ?

Coulomb’s Law Review

• Inverse-squared law

• F – Force; q1 & q2 – charges; k – constant

• d – distance between charges• Recall gravity:

• charges play the role of masses, k replaces G• http://www.colorado.edu/physics/2000/applets/nforcefield.html

221

d

qkqF

221

d

mGmF

Conservation of Charge

• Charge is conserved – neither created nor destroyed.

• This is as fundamental as momentum and energy conservation.

• When an object becomes charged, it is charge transferred from another object.

• Normally, electrons can be transferred from one object to another, not protons.

Conductors, etc.

• Metals have electrons that move very freely, while nuclei are fixed in place in the crystal lattice – they are good conductors.

• Substances like rubber and water have electrons that do not jump between atoms – they are good insulators.

• Semiconductors can behave either way.• Superconductors allow electrons to move

with virtually no resistance.

Electrical Charging

• Charging by friction or contact: electrons transferred from one body to another.

• Charging by induction:

• Induction works because charges in a conductor are separated by the forces from another nearby charge.

Charge Polarization

• When an atom is under the influence of a nearby charge, the force attracts the nucleus and repels the electron “cloud” or vice, versa.

• In any case their centers no longer coincide, and we have a polarized molecule known as a dipole (two poles).

• Some molecules (water, for example) are always polarized.

• http://www.colorado.edu/physics/2000/applets/h2o.html

Electric Field**

• A gravitational field is a force per unit mass. We think of the earth as the producer of a gravitational field, and smaller masses as feeling a force due to this field.

• The force the small (test) mass feels depends only on its own mass, given that the earth is producing the field.

• Likewise for an electric field.

Electric Field

• Think of a fixed set of charges producing a field that effects a force on some other charge.

• The electric field of these fixed charges gives a picture of the magnitude and direction of the force on a unit charge anywhere in space relative to the fixed charge distribution.

• http://www.colorado.edu/physics/2000/applets/forcefield.html• E-Field Applet

Electric Field

• We always count a test charge as positive, so field lines point toward negative charges and away from positive charges.

• Regions where the field lines are closer together are where the magnitude of the force is greater on any given charge, and if the lines are far apart, the force is weak.

Electric Field

• The electric field inside a conductor is always zero everywhere inside.

• This allows electrical shielding.

Electric Field Example 1

• Deepika pulls her wool sweater over her head, which charges her body as the sweater rubs against her cotton shirt. a) What is the electric field at a location where a 1.60 x 1019 C-piece of lint experiences a force of 3.2 x 109 N as it floats near Deepika? b) What will happen if Deepika now touches a conductor such as a door knob?

Electric Field Example 2

• A fly accumulates 3.0 x 1010 C of positive charge as it flies through the air. What is the magnitude and direction of the electric field at a location 2.0 cm away from the fly?

Electric Potential

• Recall gravitational potential energy of an object – due to its height above the ground. The potential energy is there because the Earth puts a force on the object, enabling it to do work.

• Same for electrical forces.

• Any object with a force on it has potential energy.

Electric Potential• Potential Difference: The work done to move a positive test charge

from one location to another.

• Potential Difference = Work/test charge = W/qo

• The SI unit for potential difference is the volt (V), which equals a joule per coulomb (J/C).

• Analogy, Turning on water hose

• Remember, the term “work” can be replaced with the term “energy,” because to store energy in, or give energy to, an object, work must be done.

• Therefore, potential difference can also be defined as the electrical potential energy per unit test charge.

• Voltage is often used to mean potential difference.

Electric Potential

• Electric potential takes the abstraction a step further:– Electric potential is potential energy per unit

charge.• http://webphysics.davidson.edu/physlet_resources/bu_semester2/c05_potential.html

• The unit for electric potential is the Volt.

1 volt = 1 joule / coulomb

(Coulomb is the unit for charge)

Electric Potential

• What does it mean to say that your car has a 12-volt battery?

• It means that 1 coulomb of charge that moves from one terminal to the other either does 12 Joules of work on the way, or picks up 12 Joules of kinetic energy.

• ½ coulomb will pick up 6 joules of kinetic energy. (volts x coulombs = joules)

Storing Electrical Energy

• Storing electrical energy depends on keeping positive and negative charges separated.

• This is very difficult to do, since the electrical force is so strong.

• But we can use a capacitor, which is two conducting plates separated by an insulator, to store energy in the field between the plates. (Elmo first)

• http://webphysics.davidson.edu/physlet_resources/bu_semester2/c07_capacitor_energy.html

Voltage

• The field that exists between two charged parallel plates is uniform except near the plate edges, and depends upon the potential difference between the plates and the plate separation.

• E = Voltage/distance between plates = V/x • Here, the unit for electric field is the volt/meter. It was noted earlier

that the unit for electric field is the Newton/coulomb. This means that a volt/meter must equal a Newton/coulomb?

• Volt/meter =

Electric Potential Example 1

• An electron in Tammie’s old black and white TV is accelerated toward the screen across a potential difference of 22,000 V. How much kinetic energy does the electron lose when it strikes the TV screen?

Voltage Example 2

• Amir shuffles his feet across the living room rug, building up a charge on his body. A spark will jump when there is a potential difference of 9000 V between the door and the palm of Amir’s hand. This happens when his hand is 0.3 cm from the door. At this point, what is the electric field between Amir’s hand and the door?