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Electric charge is always conserved in an isolated system – For example, charge is not created in the process of rubbing two objects together – The electrification is due to a transfer of charge from one object to another – Charge can only be separated

Conservation of Electric Charges A glass rod is rubbed with silk Electrons are transferred from the glass to the silk Each electron adds a negative charge to the silk An equal positive charge is left on the rod

The electric charge, q, is said to be quantized – q is the standard symbol used for charge as a variable – Electric charge exists as discrete packets – q = Ne N is an integer e is the fundamental unit of charge |e| = 1.6 x C Electric: q = -e-e Proton: q = +e+e

Electrical conductors are materials in which some of the electrons are free electrons – Free electrons are not bound to the atoms – These electrons can move relatively freely through the material – Examples of good conductors include copper, aluminum and silver – When a good conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material

Electrical insulators are materials in which all of the electrons are bound to atoms – These electrons can not move relatively freely through the material – Examples of good insulators include glass, rubber and wood – When a good insulator is charged in a small region, the charge is unable to move to other regions of the material

The electrical properties of semiconductors are somewhere between those of insulators and conductors Examples of semiconductor materials include silicon and germanium

Charging by induction requires no contact with the object inducing the charge

Charge Rearrangement in Insulators A process similar to induction can take place in insulators The charges within the molecules of the material are rearranged

The term point charge refers to a particle of zero size that carries an electric charge – The electrical behavior of electrons and protons is well described by modeling them as point charges

Force between two point charges is proportional to each charge inverse proportional to the squared distance between the charges k is proportionality constant (Coulomb constant)

Coulomb's Law, Notes Remember the charges need to be in coulombs e is the smallest unit of charge e = 1.6 x C So 1 C needs 6.24 x electrons or protons Typical charges can be in the µC range Remember that force is a vector quantity

In vector form, r is a unit vector directed from q1 to q2q2 The like charges produce a repulsive force between them

.The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present – Remember to add the forces as vectors The resultant force on q1 is the vector sum of all the forces exerted on it by other charges: F1 = F21 + F31 + F41

The electric force is a field force Electric Charges are the source of the electric field The electric field is defined as the electric force on the test charge per unit charge The test charge serves as a detector of the field

Electric Charges There are two kinds of electric charges – Called positive and negative Negative charges are the type possessed by electrons Positive charges are the type possessed by protons Charges of the same sign repel one another and charges with opposite signs attract one another

Electric Charges There are two kinds of electric charges  –  – Called positive and negative Negative charges are the type possessed by  electrons Positive charges are the type possessed by  protons Charges of the same sign repel one  another  another and charges with opposite signs  attract  attract one another

Field lines are tangential to the field Field lines are directed from positive charges toward negative charges The density of field lines is a measure for the field strength

The field lines radiate outward in all directions – In three dimensions, the distribution is spherical The lines are directed away from the source charge – A positive test charge would be repelled away from the positive source charge

The field lines radiate inward in all directions The lines are directed toward the source charge A positive test charge would be attracted toward the negative source charge

The charges are equal and opposite The number of field lines leaving the positive charge equals the number of lines terminating on the negative charge

The charges are equal and positive The same number of lines leave each charge since they areequal in magnitude At a great distance,the field is approximately equal to that of a single charge of 2q2q

The positive charge is twice the magnitude of the negative charge Two lines leave the positive charge for each line that terminates on the negative charge At a great distance, the field would be approximately the same as that due to a single charge of +q+q

2 Types of electric charges (pos. & neg.) Like charges repel one another Unlike charges attract one another Total amount of charge is conserved Charges move freely in conductors Charges cannot move in insulators Coulomb’s law describes force between two point charges Electric field is created by charge

Chapter-1

Quantistion of charge 1. The charge of a body q = ne; Where n is the number of charged particles and e = 1.6 x 10  19 C. 2.There are two types of charges, positive and negative. When a glass rod is rubbed with silk, the glass rod becomes positive and silk becomes negative. The glass rod and silk have equal and opposite charges. When an ebonite rod is rubbed with fur, the charge on the ebonite rod is negative and that on fur positive. Their charges are equal in magnitude.

3.Conservation of charge: The charge can be transferred from one body to another, but it can neither be charged nor destroyed: total charge is conserved 4.Additivity of charges : The total charge of a system of charges is the algebraic sum of the charges. 5.The basic properties of electric charges are (i)quantization (ii) conservation and(iii)additivity.

6.Coulomb’s Law : F = 0 0 = 8.85 x 10  12 C2 C2 /Nm 2 ; k = 9 x 10 9 Nm 2 /C 2 (in free space) 7 Charge distributions (a) Line charge density = q/l (C/m); (b) surface charge density  = q/A (C/m 2 ); (c) volume charge density p = q / v (C/m 3 ) 8 Dipole moment p = 21 x q ; ‘21’ is the length of the dipole. Its unit is mC. It is a vector whose direction is from the negative charge to the positive charge.

8 Dipole moment p = x q ; ‘ 21’ is the length of the dipole. Its unit is mC. It is a vector whose direction is from the negative charge to the positive charge.

9.Intensity of electric field. (a) Due to a point charge q distant r from it E = away from a positive charge and towards a negative charge. (b) Due to an electric dipole:- (i) At any point on its axis distant r from the center of the dipole. (ii) At any point on its equatorial line distant r from its center 10.The dipole does not experience a net force Torque on a dipole in a uniform electric field:

11.The electric flux,  = (NC -1 m2) If E is uniform over a surface,  = If the surface of area A is perpendicular to the uniform field lines,  = EA. 12.Gauss’ theorem states that the electric flux through any closed surface in free space is times the total charge enclosed by the surface  = or

13.Field due to a line charge of linear charge density E= 14.Field due to an infinite sheet of uniform surface-charge-density  E=

15.Field due to a conducting spherical shell of radius. R and total charge 1q are at a distance r from its center. (i) E = (ii) E = (iii) E = 0 ; if r < R The same is the case with a conducting sphere because, when the conducting sphere is charged, the charge is uniformly distributed over its surface. 16.Electric potential at a point is the work done to bring a unit positive charge from infinity to the point. Unit: volt (V). It is a scalar quantity. 17.The p.d between any two points A and B is the work done to bring a unit positive charge from A to B V AB = VB VB  VA VA =  the negative line integral of the electric field from A to B.

18Potential at any point due a point charge, V = (1/4  0 ) x 19Even though the potential at a point is a scalar, the potential due to a positive charge is positive and that due to a negative charge is negative. 20Electric field (E) at any point is the negative gradient of the electric potential at that point E = - (dV/dr) V = (1/4  0 )

21Electric potential due to a system of n charges. V=(1/4  0 ) 22.The electric potential inside a charged conducting sphere (solid or hollow) is the same as that on its surface. 23.Electric potential due to an electric dipole, V=(1/4  0 )x. On the axial line,  = 0, and on the equatorial line  = 90 0.

24.Equipotential surface is a surface where the electric potential is same at every point on the surface. Ex : surface of a charged conductor. 25Electric potential energy due to a system of two charges U=(1/4  0 ). 26.Electric potential energy of a dipole placed in an electric field, U =. When a dielectric medium (polar or non-polar) is placed in an electric field, it acquires a net dipole moment. This phenomenon is called dielectric polarisation.

27.For a conductor of charge Q and potential V, Q  V or Q = C V, where C is a constant called the capacitance (or capacity) of the conductor. 28.A condenser (or capacitor) is an arrangement of conductor. If there are two conductors at potential difference V and charge + Q and – Q, C = Q / V. 29Capacitance of a parallel plate condenser (a) with air between the plates is C =  0 A/d; and with a dielectric medium of dielectric constant K is C = K  0 A/d. 30.When capacitors are in series 1/C ef f = 1/C 1 + 1/C ; and in parallel C ef f = C1 C1 + C 2 + C 3 + ……. 31.Energy stored in the electric field between the plates of a capacitor, i.e., potential energy, U=(1/2)CV 2 = (1/2)QV = (1/2) Q 2 /C.