Electrical Potential Energy

The difference in potential energy between two points is equal to the negative of Work done by a force 

ΔU = -W_ab

Above equation is possible only for conservative forces which means that potential energy can only be defined for conservative forcesForces are conservative if and only if the work done by these forces when a body moves from a to b is independent of the path taken between these two locationsFor example work done by a force in the gravitational field is independent of the path followed by the particle We can make a similar argument for the electrostatic force with the same result Which means that the electrostatic force is also conservative and can be demonstrated by potential energy The only difference between the two is that gravitational force is only attractive and electrostatic force can be attractive and repulsive both.

Consider  system of two positive charges +q and q₀

The charge q₀ moves under the influence of E field created by +q

The charge q₀ moves a small displacement dr as it moves from position A to position B

Magnitude of E field created by +q decreases as the charge q₀ moves farther away from charge +q

The charge q₀ experiences a force (F = q₀ E ) that varies with displacement

We need to calculate work done by a variable force

ELECTRIC FLUX AND GAUSS"S LAW

 The word “flux” comes from the latin word meaning “to flow”

 For a vector field flux is the number of lines passing through a surface

Mathematically it is the product of the surface area  “A” and the component of the electric field “E” perpendicular to the surface

ΦE = EA Nm2 /C

If  area “A” is not exactly perpendicular to the electric field E

ΦE = EAcosf

Flux will be maximum when surface area is perpendicular to the electric field

ΦE = EA

Gauss's Law

The total electric flux through any closed surface is proportional to the total electric charge inside the surface

electric and gravitational field

Gravitational Field:

It is the gravitational force per unit test mass m_o  and is represented by g

                                                g = F/m_o                                              

Ø   This field is static, because the source of the field i.e. the mass of the gravitating body is constant

Ø   This field is also uniform meaning that g is same (in direction and in magnitude) for all the points

 This field is independent of the magnitude of test mass m_o (because the small mass m_o will not disturb the distribution of  the mass of gravitating body.
Electric Field:

This field is independent of the magnitude of test mass m_o (because the small mass m_o will not disturb the distribution of  the mass of gravitating body.The space around a source charge where a test charge can experience an electric force is called the electric field. The electric field at a point in the vicinity of source is the electric force F_o experienced by the test charge q_o at that point divided by the charge q_o.  The direction of electric field E is the same as the direction of electric force F_e because q_o is a positive scalar quantity.Units of the electric field in SI units is Newton/Coulomb (N/m) and some time it may also be given as volt/meter V/m

Field and its types

Faraday introduced the concept of field, which he defined as a space surrounding an object, such as an electron or magnet, in which other objects are subject to (or affected by) a force

In general we can define field as

Ø   Is a way to depict effects or

Ø   It is some thing that can be define anywhere in space or

Ø   Field can represents a physical quantity like temperature, fluid, wind speed, pressure and force (electric, magnetic and gravitational)

There are three main types of Fields:

Ø  Scalar field: (independent of spatial variation)

e.g. Temperature and pressure field

Ø   Static field: Independent of time variation

e.g. All types of field that don’t vary with time

Ø   Vector field: Varying with position

e.g. electric and magnetic field

Coulomb's law

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

Valid only when objects are small size particles and distance between them is large as compared to their sizes

The Coulomb’s Law can be mathematically expressed as

F= ( q₁   * q₂₎ / r²

F is the force of attraction or repulsion, measured in Newton 

k is the Universal Electrostatic Constant, equal to 9 ´ 10⁹ N m²/C²

q₁ and q₂ are the magnitudes of charges, measured in C

r is the distance between the charges, and is measured in m where K is proportionality constant which depends upon the medium i.e. ε_o 

ways to charge materials

Charging by friction - this is useful for charging insulators. If you rub one material with another (say, a plastic ruler with a piece of paper towel)

Charging by conduction - useful for charging metals and other conductors. If a charged object touches a conductor, some charge will be transferred between the object and the conductor, charging the conductor with the same sign as the charge on the object.

Charging by induction - also useful for charging metals and other conductors. Again, a charged object is used, but this time it is only brought close to the conductor, and does not touch it.

types of material

Conductors:

                 Are materials that allow an electric current to flow through them easily i.e. the charges are free to move in these materials.  Most metals are good conductors.

Insulator:

                Substances that do not allow electric current to flow through them are called insulators, nonconductors, or dielectrics. Rubber, glass, and air are common insulators. However, if an object contains a sufficient amount of charge, the charge can arc, or jump, through an insulator to another object.