eletri charges notes

ELECTROSTATICS ELECTRIC CHARGE: Charge is something possessed by material objects that makes it possible for them to exert electrical force and to respond to electrical force. FRICTIONAL ELECTRICITY: The property of rubbed substances due to which they attract light objects is called electricity. The electricity developed by rubbing or friction is called frictional or static electricity. The rubbed substances which show this property of attraction are said to have become electrified or electrically charged. BASIC PROPERTIES OF ELECTRIC CHARGES: Relativistic Invariance: Charge on a body is relativistically invariant. i.e. charge on a body at rest equals the charge on the body at relativistic speed. However charge density is not relativistically invariant. Additivity of electric charge: This means that the total charge of a system is the algebraic sum of all the individual charges located at different points inside the system. QUANTISATION OF CHARGE: All free charges are integral multiple of basic unit of charge represented by ‘e’. Thus charge q is given by q=ne. Law of conservation of charge: when bodies are charged through friction, there is only transfer of charge from one body to another but no net creation or destruction of charge takes place. COULOMB’S LAW: It states that the force of attraction or repulsion between two point charges at rest is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The force acts along the line joining the two charges. SUPERPOSITION PRINCIPLE: For many charges, the force on any single charge is the vector sum of the forces due to each other charge on it. ELECTRIC FIELD: It is the region (three dimensional) around a charge in which its electrical influence can be realized. FIELD DUE TO A POINT CHARGE: Consider a point charge q placed in vacuum. The force on a test charge q0 placed at a distance r from q is: . FIELD DUE TO SEVERAL POINT CHARGES: Suppose we have several point charges q1,q2.......qn fixed at different points in space. Then, according to the superposition principle, the electric field E at a given point is the vector sum of the fields due to all the charges: Electric DIPOLE: An electric dipole consists of a pair of equal and opposite point charges separated by some small distance. ELECTRIC FIELD DUE TO A DIPOLE ON THE AXIS: The direction of the electric field on axial point will be along the axis of the dipole from negative towards the positive charge which is the same as the direction of P. This position is also called End on Position In vector notation, ELECTRICAL FIELD AT THE AXIS OF A CIRCULAR UNIFORMLY CHARGED RING: TORQUE EXPERIENCED BY ELECTRIC DIPOLE IN UNIFORM ELECTRIC FIELD: The magnitude of torque is given by; Torque, ( = Force x arm of the couple = F x BC = (qE) 2a sin ( ( = PE sin ( ( P = q x 2a) The above expression can be written in vector form as : Workdone in rotating electric dipole in uniform electric field: This work done is stored in the dipole in the form of potential energy (U). Potential energy of dipole, U = -PE cos ( In vector form, ELECTRIC LINES OF FORCE: We may define an electric field line as a path, straight or curved, such that tangent to it any point gives the direction of electric field intensity at that any point. PROPERTIES OF ELECTRIC LINES OF FORCE: 1.Tangent to the electric field line at any point gives the direction of electric intensity at that point. 2.No two lines of force can intersect each other. 3.Electric field lines are always normal to the surface of the conductor. 4.The electric field lines contract longitudinally. 5.the electric lines exert a lateral pressure. FIELD DUE TO INFINITE LINE OF CHARGE: The electric field due to infinite line of charge is given by the relation, The electric field, due to an infinite line charge, varies as the inverse of the distance of the field point (from the line charge). The direction of the field is, along the normal to the line charge, passing through the field point. Field due to a thin plane infinite sheet of charge: The electric field due to thin plane infinite sheet of charge is given by the relation, The field of an infinite plane sheet of charge is, field of constant magnitude directed along the normal to the sheet. Field due to uniformly charged spherical shell: The field due to uniformly charged spherical shell is given by, The field therefore, has its maximum value at the surface of the sphere. Electric potential: Potential at a point is the work done (by external agent) in moving a unit positive charge from infinity to that point. Thus, if the work done in moving a charge q0 from infinity to a point is W, then potential at that point is Electric potential due to a point charge: Electric potential at a point in the electric field of a field charge, is defined (or measured) as the work done in moving a unit positive (test) charge from infinity. Potential due to dipole at any point: Potential due to dipole at any point is given by, If for axial position, And if for equatorial position, Potential due to a number of point charges: The potential at any point p due to point charges q1, q2, . . ., qn at distances r1, r2,. . . ,rn respectively from P is algebraic sum of the potentials at P due to individual charges, i.e., POTENTIAL DUE TO A SHELL: Consider a shell of charge Q having a radius R. The potential due to the shell at a distance r from its centre is constant inside the shell (r