**Electric, Magnetic, and Gravitational Fields**

**Electrical Fields**

**Magnetic Fields and Electromagnetism**

**Gravitation Field**

**Detail 3**

Detail 4

* Opposites electric charges attract each other.

* Similar electric charges repel each other.

* Charged objects attract some neutral objects.

The Laws of Electric Charge

Charging By Friction

An atom holds on to its electrons by the force of electrical attraction to its oppositely charged nucleus

i.e when ebonite and fur are rubbed together, some electrons in the fur have a stronger attraction from atomic nuclei in the ebonite then they do from nuclei in the fur

Induced Charge Separation

Distribution of charge that results from a change in the distribution of electrons in or on an object.

Charging by Contact

When you take a charged ebonite rod and it comes in contact with a neutral pith ball, some excess electrons on the rod are repelled by the proximity of their neighboring excess electrons move towards the pith ball. The pith ball and the ebonite rod share the excess of electrons that the charged rod have before and both now have some extra making them both negatively charged

Charging by Induction

Law of Conservation of Charge

The total charge (the difference between the amounts of positive and negative charge) within an isolated system is conserved

Summary

* The laws of electric charge state: opposite electric charges attract each other; similar electric charges repel each other; charged objects attract some neutral objects.

* There are three ways of charging an object: by friction, by contact, and by induction

Electric Forces:

Coulomb's Law

In 1785, French physicist Charles Augustin de Coulomb experimented the quantitative nature of the electric force between charged particles, it was widely expected to be an inverse square law. Coulomb's apparatus contained a silver wire attached to the middle of alight horizontal insulating rod. One end of the rod was pith ball covered in gold foil. At the other end, to balance the rod, a paper disk was attached. Coulomb took an identical stationary ball into contact with the suspended ball. He charged both balls then repelled each other, twisting the wire holding the rod until coming to, r, some distance away. Thus Coulomb knew how much force was required to twist his wire through any angle, he showed that the magnitude of this electric force was inversely proportional to the square of the distance between the centres of his changed spheres.

History

Coulomb's Law

The force between two point charges is inversely proportional to the square of the distance between the charges and directly proportional to the product of the charges.

Important Equations

* Magnitude of electric force is directly proportional to the product of the magnitudes of the charges on each sphere

* Magnitude of electric force is inversely proportional to the square of the distance, r, between the centres of his charged spheres

Electric Charge is Measured in Coulombs

Sample Problem 1

Coulomb`s Law v.s

Law of Universal Gravitation

Similarities

* Both are inverse square laws that are also proportional to the product of another quantity; for gravity it is the product of two masses, and for the electric force it is the product of the two charges.

* The forces act along the line joining the centres of the masses or charges.

* The magnitude of the force is the same as the force that is measured if all the mass or charge is concentrated to a point at centre of sphere. Thus, distance in both cases is measured from the centre's of the spheres (assuming that

r

is longer than the radius of the object).

Differences

* The electric force attracts or repels, according to the charges involved, whereas the gravitational force can only attract.

* The universal gravitational constant is small where the gravitational force can be ignored unless at least one of the masses is very large. But in Coulomb`s constant k, it is a larger number (over one hundred billion billion times bigger than G) therefore if even small charges can result in noticeable forces.

Sample Problem 2

Summary

* Coulomb`s law states that the force between two point charges is inversely proportional to the square of the distance between the charges and directly proportional to the product of the charges

* Coulomb`s law applies when the charges on the two spheres are very small, and two spheres are small compared to the distance between them.

Electric Fields

Field Theory

The theory that explains interactions between bodies or particles in terms of fields

Field of Force

A field of force exists in a region of space when an appropriate object placed at any point in the field experiences a force.

Sample Problem 3

Electrostatic Precipitators

- Air pollution control devices that remove tiny particles from the emissions of processing and power plants that burn fossil fuel. Relying on the properties of electric fields, the devices can remove almost all about 99% of the tiny particles of soot, ash, and dust.

Electric Fields in Nature

A lot of animals detect weak electric fields. For example a goby fish will hide from sharks in small holes. Though the hammerhead cannot see the goby, it can detect electric fields caused by movement and breathing. The electric field produced by the goby will extend about 25 cm above the sand giving away it`s presence.

Summary

* A field of force exists in a region of space when an appropriate object placed at any point in the field experiences a force.

* The electric field at any point is defined as the electric force per unit positive charge and is a vector quantity.

* Electric field lines are used to describe the electric field around a charged object. For a conductor in static equilibrium, the electric field is zero inside the conductor; the charge is found on the surface; the charge will accumulate where the radius of curvature is smallest on irregularly-shaped objects; the electric field is perpendicular to the surce of the conductor

Electric Potential

Electric Potential Energy

The energy stored in a system of two charges a distance r apart;

Electric

Potential

Energy

NOTE

The sign for electric potential energy could be positive or negative depending on the sign of the charges. If q 1 or q 2 are opposite charges they attract then the expression is correct giving the electric potential a negative value. If q 1 and q 2 are similar charges they repel and expect the electric potential energy to be positive.

Electric Potential

The value in volts of potential energy per unit positive charge; 1 V = 1 J/C

Note: 1 V is the electric potential at a point in electric field if 1 J of work is required to move 1 C of charge from infinity to that point; 1 V = 1 J/C

Sample Problem 4

Medical Applications of Electric Potential

To have a good understanding of the human nervous system one must know the concept of electric potential. The nerve cell or neuron contains a cell body with short extensions and a long stem which branches into many nerve endings. The dendrites convert external stimuli in electrical signals which travel through the neuron toward the nerve endings. The electric signals then cross a gap between the nerve ending and next cell in the transmission chain. The fluid in the nerve cell has high concentrations of negatively charged proteins. The extracellular fluid contains high concentrations of positive sodium ions. The difference in concentration is because of selectively permeable membrane that surrounds the cell, causing a buildup of equal amounts of negative charge inside and positive charge outside the cell membrane. This charge separation gives rise to an electric potential difference across the membrane.

SUMMARY

* The electric potential energy stored in the system of two charges q 1 and q 2 is

* The electric potential a distance r from the charge q is given by V= kq/r.

* The potential difference between two points in an electric field is given by the charge in the electric potential energy of positive charge as it moves from one point to another.

* The magnitude of the electric field is the charge in potential difference per unit radius

Determining the Elementary Charge

Sample Problem 5:

The Millikan Experiment

* The smallest unit of electric charge, called the elementary charge, e, of which other units are simple multiples; e= 1.602 x 10 to the power of -19 C.

The motion of charged particles in Electric Fields

Example 6:

Inkjet Printer's

Inkjet projector's use charged parallel plates to deflect droplets of ink going towards the paper

The Motion of Charged Particles in Electric Fields

* A charged particle in a uniform electric field moves with uniform acceleration.

* From conservation particles, any changes to a particle's kinetic energy result from corresponding changes to its electric potential energy (when moving in any electric field, ignoring gravitational effects).

Magnets

When bar magnet is dipped in iron filings, fillings are attracted to it, going mostly towards the regions at the end of the magnet-the poles. When bar magnet rotates freely the pole that seeks in the northerly direction is called the north-seeking pole, or the N-pole. The other is called the south-seeking pole or S-pole

Law of Magnetic Fields

Opposite magnetic poles attract. Similar magnetic poles repel.

Magnetic Fields

Magnetic Force Fields

The area around a magnet in which magnetic forces are exerted.

Earth's Magnetic Field

Sir William Gilbert, english physicist determined that Earth's magnetic field resembled the field of a large bar magnet, inclined at a slight angle to Earth's axis with the S-pole in the northern hemisphere.

Domain Theory of Magnetism

Theory that describes, in terms of tiny magnetically homogeneous regions ("domains"), how a material can become magnetized: each domain acts like a bar magnet.

Principle's of Electromagnetism

Moving electric charges produce a magnetic field.

Magnetic Field of a Straight Conductor.

When an electric current flows through along, straight conductor, the resulting magnetic field consists of field lines that concentric circles, centered on the conductor.

Right Hand Rule for a Straight Conductor

If a conductor is grasped in the right hand, with the thumb pointing in the direction of the current, the curled fingers point in the direction of the magnetic field lines

Magnetic Field of a Current Loop

Magnetic Field of a Coil or Solenoid

A solenoid is along conductor wound into a coil of many loops.

Right-Hand Rule for a Solenoid

If a solenoid is grasped in the right hand, with the fingers curled in the direction of the electric current, the thumb points in the direction of the magnetic field lines in its core.

Natural Magnetism and Electromagnetism

The law of magnetic poles state that opposite magnetic poles attract and similar magnetic poles repel.

A magnet surrounded by a magnetic force field.

The principle of electromagnetism states that moving electric charges produce a magnetic field.

Measuring Magnetic Fields

Sample problem:

A physical theory which employs fields in the physical sense, consisting of two types:

Classical field theory, the theory and dynamics of classical fields.

Quantum field theory, the theory of quantum mechanical fields.

Field Theory

Magnetic Fields on Moving Charges

A current can exert force on a magnet, and a magnet can exert force on a current.

The direction of the magnetic force is given by the right-hand rule.

Magnetic Force on a Conductor

A beam of charged particles moving through a magnetic field in a vacuum experiences a magnetic force. This also occurs inside a conductor.

Right-Hand Rule for the Motor Principle

If the right thumb points in the direction of the current (flow of positive charge), and the extended fingers point in the direction of the magnetic field, the force is in the direction in which the right palm pushes.

Sample Problem

Magnetic Force on a Conductor

The magnitude of the force on the conductor F is in a direction perpendicular to both the magnitude of the magnetic field B and the direction of the current I.

Reversing either the current direction on the magnetic field reverses in the direction of the force

Ampere's Law

Along any closed path through a magnetic field, the ism of the products of the scalar components of B, parallel to the path segment with the length of the segment , is directly proportional to the net electric current passing through the area enclosed by the path.

Sample Problem

Law of Electromagnetic Induction

An electric current is induced in a conductor whenever the magnetic field in the region of the conductor changes time

Lenz's Law

When a current is induced in a coil by changing magnetic field, the electric current is in such a direction that its own magnetic field opposes the change that produced it.

Gravitational Field

Exists in the space surrounding an object in which the force of gravity exists.

Sample Problem

Gravitational Fields

A gravitational field exists in the space surrounding an object in which the force of gravity is exerted on objects.

The magnitude of the gravitational field strength surrounding a planet or other body (assumed to be spherical) is directly proportional to the mass of the central body, and inversely proportional to the square of the distance to the center of the body.

The law of the universal gravitation applies to all bodies in the solar system, from the Sun to planets, moons, and artificial satellites.

Kepler's First Law of Planetary Motion

Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse.

Kepler's Second Law of Planetary Motion

The Straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time.

Kepler's Third Law of Planetary Motion

The cube of teh average radius r of a planets orbit is directly proportional to the square of the period T of the planet's orbit.

Sample Problem

Gravitational Potential Energy Problem

Escape from a Gravitational Field

Escape speed- the minimum speed needed to project a mass m from the surface of mass M to just escape the gravitational force of M.

Escape Energy- The minimum kinetic energy needed to project a mass m from the surface of mass M to just escape the gravitational force of M.

Binding energy- the amount of additional kinetic energy needed by a mass m to just escape from a mass M.

Sample Problem

Gravitational Potential Energy in General

The gravitational potential energy of a system of two (spherical) masses is directly proportional to the product of their masses, and inversely proportional to the distance between their centers.

A gravitational potential energy of zero is assigned to an isolated system of two masses that are far apart that the force of gravity between them has dropped to zero.

The change in gravitational potential energy very close to Earth's surface is special case of gravitational potential energy in general.

Escape speed is the minimum speed needed to project a mass m from the surface of mass M to just escape the gravitational force of M.

Escape energy is minimum kinetic energy needed to project a mass m from the surface of mass M to just escape the gravitational force of M.

Binding energy is the amount of additional kinetic energy needed by mass m to just escape from a mass M.