ELECTRIC CHARGES AND FIELDS
1.1 INTRODUCTION Electrostatics deals with the study of forces, fields and potentials arising from static charges 1.2 ELECTRIC CHARGE By convention, the charge on electron is considered as negative & the charge on proton is considered as positive. If we say that a body is charged, it means body have excess or deficit of electrons. A body having negative charge implies that body has excess of electrons. A body having positive charge implies that body is deficient of electrons. In solids, some of the electrons, being less tightly bound in the atom, are the charges which are transferred from one body to the other. A body can thus be charged positively by losing some of its electrons. Similarly, a body can be charged negatively by gaining electrons. The SI unit of electric charge is coulomb
Metal knob Metal rod Rubber It is a device used to detect the nature and amount of electric charge present in a charged body. It consists of a vertical metal rod housed in a box, with two thin gold leaves attached to its bottom end. When a charged object touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. The degree of divergance is an indicator of the amount of charge. Glass window Gold leaves Gold Leaf Electroscope
. 1.3 CONDUCTORS AND INSULATORS Charging by Friction: .When certain insulators are rubbed with cloth or fur, they become electrically charged due to the transfer or charge or electrons. As the two objects are rubbed together, one object loses electrons while the other gains electrons. There is a transfer of electrons from one object to the other. The object that gains electrons becomes negatively charged, while the object that loses electrons has an excess of positive charge. Hence it is positively charged. The transfer of charge is due to the contact between the materials, and the amount of charge transferred depends on the nature of these materials.
1.4 CHARGING BY INDUCTION Induction is the process by which a uncharged body is charged by using a charged body without actual contact between them or losing its own charge. If a charged body is brought near a neutral body, the charged body attracts opposite charge and repels similar charge present on the neutral body. Afterwards, the neutral body is earthed and the like charge is neutralised by the flow of charge from earth leaving unlike charge on the body. Now the earthing and the charging body are removed leaving the initially neutral body charged.
. Charging by Conduction: In the process of charging by conduction, direct contact of charged and uncharged body is involved and both objects acquire the same kind of charge. If a negative object is used to charge a neutral object, then both objects become charged negatively and vice versa.
1.5 BASIC PROPERTIES OF ELECTRIC CHARGE 1.5.1 Additivity of charges If a system contains two point charges q and q2, the total charge of the system is obtained simply by adding algebraically q1 and q2,l.e, charges add up like real numbers or they are scalars like the mass of a body. If a system contains n charges q1, q2, q, .., In, then the total charge of the system is q1+2+ 93+ 1.5.2 Charge is conserved Within an isolated system consisting of many charged bodies, due to interactions among the bodies, charges may get redistributed but it is found that the total charge of the isolated system is always conserved .1.5.3 Quantisation of charge Experimentally it is established that all free charges are integral multiples of a basic unit of charge denoted by e. Thus charge q on a body is always given by q n e, here n is any integer, positive or negative. This basic unit of charge is the charge that an electron or proton carries. By convention, the charge on an electron is taken to be negative; therefore charge on an electron is written as -eand that on a proton as te. (e 1.602192 x 10-19 C)
1.6 COULOMB'S LAW According to this law "The magnitude of the electric force between two static point charges, in vacuum, is directly proportional to the product of the magnitude of the two charges and inversely proportional to the square of the distance between them and acts along the straight line joining the two charges". The magnitude of Coulomb's law is given by the expression: . Where, F is the force between two point charges, q1 and q2 are magnitude of charges, r is the distance between these charges. q 2 r2
Some facts about Coulomb's law: charges in motion. third law of motion neighborhood; hence, the principle of superposition is valid. Coulomb's law should be used for point charges in vacuum at rest. It is not valid for The electrostatics force acts along the line joining the two charges. It obeys Newton's Coulomb's force is not affected by the presence of other charges in the Force between like charges is repulsive and between unlike charges attractive
Coulomb's law in vector form: 492 F21 = are, gira [when 919.> 0], te. charges are like charges 1 h:4 1e, ri2 [when qA2 <O], ie.charges arelikecharges ATE Here F, is force on q, by q, and Fi is vector pointing from a, to q, e, is called absolute electrical pennittivity of free space 9x109 N C"
1.7 FORCES BETWEEN MULTIPLE CHARGES Superposition Principle The net force on any charge (g) due to any number of charges (i,99q..) at rest is the vector sum ofall the forces on that charges, taken one at a time. Here, Fo is the total force on charge go Fo1 is force on go due to qi Foz is force ong, due to g All of electrostatics is basically a consequence of Coulomb's law and the superposition principle Fon is force on go due to ga
1.8 ELECTRIC FIELD .Electric field due to a given charge is the space around the charge in which electrostatic force of attraction or repulsion due to the charge can be experienced by any other charge. Source Charge & Test Charge: The charge which produces electric field is known as source charge. Charge (generally written as qo) which tests the effect of source charge is called test charge. Electric Field Intensity: .Electric filed intensity at any point is the strength of electric field at that point. It is defined as the force experienced by unit positive charge placed at that point.
Electric field intensity at any point due to a group of point charges: Electric field intensity at any point due to a group of point charges is equal to the vector sum of electric field intensities due to individual charges at the same point.
1.10 ELECTRIC FLUX electric flux is the measure of the distribution of the electric field through a given surface the number of field lines proportional to E AS cost. lines will be parallel to AS at all crossing AS is When 90, field and will not cross it
(i) For points on the axis Let the point P be at distance r from the centre of the dipole on the side of the charge q where "p is the unit vector along the dipole axis (from -q to q) The total field at P is 4 ar For r>a 3
(ii) For points on the equatorial plane The magnitudes of the electric fields due to the two charges +a and -a are aiven by Clearly, the components normal to the dipole axis cancel away. The components along the dipole axis add up. The total electric field is opposite to p E at P cose P 2qa cl At large distances (r>> a), this reduces to 2 q a
The dipole moment vector p of an electric dipole is defined by at large distances takes simple form At a point on the dipole axis 2p At a point on the equatorial plane (r>> a the important point that the dipole field at large distances falls off not as 1/r 2 but as1/r 3