ELECTRIC CHARGE AND ELECTRIC FIELD

• The negatively charged electrons are held within the atom by the attractive Electric forces exerted on them by the positively Charged Nucleus

• The protons and neutrons are held within the stable atomic nuclei by an attractive interaction, called the strong nuclear force, that overcomes the electric repulsion of the protons

• The charges of the electron and proton are equal in magnitude• In a neutral atom the number of electrons equals the number of protons in

the nucleus, and the net electric charge (the algebraic sum of all the charges) is exactly zero

• The number of protons or electrons in a neutral atom of an element is called the atomic number of the element.

• If one or more electrons are removed, the remaining positively charged structure is called a positive ion. A negative ion is an atom that has gained one or more electrons

• Electric Charge Is Conserved• The algebraic sum of all the electric charges

in any closed system is constant.• The total electric charge on the two bodies

together does not change. In any charging process, charge is not created or destroyed; it is merely transferred from one body to another.

• Important examples of the conservation of charge occur in the radioactive

• decay of nuclei, in which a nucleus transforms into (becomes) a different type of

• nucleus. For example, a uranium-238 nucleus (238U) transforms into a thorium-

• 234 nucleus (234Th) by emitting an alpha particle.

• 92U238 ------ 90Th234 + 2He4

• 1H1 + 17Cl35 ------ 16S32 + 2He4

in both cases net charge is constant Before and after change

• The magnitude of charge of the electron or proton is a natural unit of charge.

• Every observable amount of electric charge is always an integer multiple of this basic unit. We say that charge is quantized

• and electric charge can't be divided into amounts smaller than the charge of one electron or proton

• i.e. electric charge on a body either +ve or –ve is always integral multiple of electric charge of an electron or proton

• Mathematically: q = ± ne• Where n is called quantum no.

Quantization Of Charge

Conductors, Insulators, and Induced Charges

• Some materials permit electric charge to move easily from one region of the material to another, while others do not.

• Most metals are good conductors, while most nonmetals are insulators.

• Some materials called semiconductors are intermediate in their properties between good conductors and good insulators

• There are three ways that objects can be given a net charge. • 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), electrons have a tendency to be transferred from one material to the other. For example, rubbing glass with silk generally leaves the glass with a positive charge;

• 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 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.

Coulomb’s Law

The magnitude of the electric force (sometimes called the Coulomb force) between two point charges is given by Coulomb’s law

• The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space is the measure of the resistance when forming an electric field in the free space.

• The permittivity of free space (or a vacuum), e0, has a value of 8.9 × 10-12 C2/Nm2

• The permittivity of a material is usually given relative to that of free space, it is known as relative permittivity, er.

• Relative permittivity, er

• Vacuum 1 (by definition) Air 1.0005 ,Polythene 2.35, Perspex 3.3, Water 80

The Electric Field• An electric field is said to exist in the region

or space around a charged object, the source charge.

• When another charged object—the test charge—enters this electric field, an electric force acts on it

• the electric field vector E at a point in space is defined as

E has the SI units of newtons per coulomb (N/C)

• the direction of E is that of the force F that acts on the positive test charge

• Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate)

Electric Field of Point Charge

two charges that are equal in magnitude but of opposite sign, a configuration that we call an electric dipole

Electric Field Due to a Point Charge

• To find the electric field due to a point charge q at any point at distance r from the point charge, we put a positive test charge qo at that point.

The direction of E is the same as that of the force on the positive test charge

the net force Fo from the n point charges acting on the test charge is

where the integration is over the entire charge distribution

Electric Flux

• This rate of flow through an area is a flux • the total number of lines penetrating the

surface is proportional to the product EA

Electric flux is proportional to the number of electric field lines penetrating some surface.

• Consider a general surface divided • into a large number of small elements, each

of area ∆A• The electric flux through the element i

• Summing the contributions of all elements gives an approximation to the total flux through the surface:

is a surface integral, which means it must be evaluated over the surface

Gauss’s Law• we describe a general relationship between the net electric flux

through a closed surface (often called a gaussian surface) and the charge enclosed by the surface.

• Consider a positive point charge q located at the center of a sphere of radius r

we know that the magnitude of the electric field everywhere on the surface of the sphere is E= k q/r2

. The field lines are directed radially outward and hence are perpendicular to the surface at every point on the surface. That is, at each surface point, E is parallel to the vector ΔA

FE = ò E . dA = ò E dA cos f

= ò  E dA = E ò dA = E (4p R2)

= (1/4p eo) q /R2) (4p R2)

= q / eo. So the electric flux 

FE = q / eo. 

Now we can write Gauss's Law:

FE = ò E . dA = ò |EdA| cos f =Qencl

/eo

Electric FLUX through a sphere centered on a point charge q.

the net flux through any closed surface surrounding a point charge q is given by q/ϵ0 and is independent of the shape of that surface.

• The mathematical form of Gauss’s law is a generalization of what we have just described and states that the net flux through any closed surface is

where E represents the electric field at any point on the surface and qin represents the net charge inside the surface

In above Equation the charge qin is the net charge inside the gaussian surface, E represents the total electric field, which includes contributions from charges both inside and outside the surface

Application of Gauss’s Law to Various Charge Distributions

• Gauss’s law is useful for determining electric fields when the charge distribution is highly symmetric

• Spherically Symmetric Charge DistributionAn insulating solid sphere of radius a has a uniform volume charge density ρ and carries a total positive charge Q Calculate the magnitudeof the electric field at a point outsidethe sphere

• Because the charge is distributed uniformly throughout the sphere, the charge distribution has spherical symmetry and we can apply Gauss’s law to find the electric field

• Let’s choose a spherical gaussian surface of radius r, concentric with the sphere

• Everywhere on the surface and E .dA= E dA(E // to dA)

By symmetry, E is constant everywhere on the surface

• Find the magnitude of the electric field at a point inside the sphere. In this case, let’s choose a spherical gaussian surface having radius r < a, concentric with the insulating sphere Let V’ be the volume of this smaller sphere. To apply Gauss’s law in this situation, recognize that the charge q in

within the gaussian surface of volume V’ is less than Q

This says that the feld is zero at the center and increases linearly as weGo out toward the edge

Therefore, the value of the field is the same as the surface is approached from both directions

A Cylindrically Symmetric Charge Distribution

• Find the electric field a distance r from a line of positive charge of infinite length and constant charge per unit length λ

Because the charge is distributed uniformly along the line, the charge distribution has cylindrical symmetry and we can apply Gauss’s law to find the electric field

This result shows that the electric field due to a cylindrically symmetric charge distribution varies as 1/r, whereas the field external to a spherically symmetric charge distribution varies as 1/r2

Planar Symmetry

• Planar symmetry means that the charge distribution is same on the sheet.

At each point, E is perpendicular to the sheet

having same magnitude at any given distance on either side of the sheet.

• The charged sheet passes through the middle of the cylinder's length, so the cylinder ends are equidistant from the sheet

• At each end of the cylinder, E is perpendicular to the Surface the flux through each end is + EAE is parallel to the curved side walls of the cylinder, so there is no flux

through these walls. The net charge within the Gaussian surface is the charge Per unit area multiplied by the sheet area‘σ’ is charge density

Since we are considering an infinite sheet with uniform charge density, this eqn holds for any point at a finite distance from the sheet.

Field between two parallel charge plates

• The fields due to the two sheets of charge (one on each plate) are E I and E2, both of these have magnitude /2 є0

• The total (resultant) electric field at any point is the vector sum E = E I + E 2

• Since the plates are conductors, when we bring them into this arrangement, the excess charge on one plate attracts the excess charge on the other plate, and all the excess charge moves ontothe inner faces of the plates• Since no excess charge is left on the outer faces, the electric field to the left and right of the platesis zero.

• With twice as much charge now on each inner face, the new surface charge density on each inner face is twice -