## Electric Charge

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• ### Akhilesh K

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Class XII Notes On Electric Charge

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ELECTRIC CHARGE Nons CLASS 12 CBSE Electric charge and its characteristic (i) Electric charges is the fundamental intrinsic property due to which electric force acts (ii) Electric charges are two types. Traditionally charge on proton is positive and charge on electron negative. Magnitude of charge on both is same 1.6XIO 19C (iii) Fundamental charge is the charge on the electron or proton denoted by e. (iv) Quantization of charges: Magnitude of all charges are found to be integral multiple of fundamental charge thus If Q is total charge then Q = ne here n = 1, 2, 3 (v) Law of conservation of electric charge state that "The algebraic sum of electric charge in an electrically isolated system always remains constant irrespective of any process taking place. Or in other words "In an electrically isolated system only those processes are possible in which charges of equal magnitude and opposite types are either produced or destroyed. Example Before rubbing glass rod on silk algebraic sum of charge is zero. On rubbing and separating the rod from silk, we find equal and opposite amount of charge is developed on silk and glass rod. (vi) Two charges exerts equal and opposite force on each other. Like charges repeals while unlike attracts (vii) S.l Unit of charge is "coulomb' denoted by C. CGS unit of charge esu 1 coulomb = (viii) Charge cannot exists without mass though mass can exist without charge (ix) Charge is invariant: This means that charge is independent of frame of reference. i.e. change of the body does not charge with whatever be its speed Ways of charging body (A) Charging by friction: When two bodies are rubbed together, a transfer of electrons take place from one body to another. The body from which electrons have been transferred is left with an excesses of positive charge, so get positively charged. The body which receives the electrons becomes negatively charged. "The positive charge and negative charges produced by rubbing are always equal in magnitude" When glass rod is rubbed on silk, glass rod loses its electrons and gets positive charges, while silk acquires equal negative charges. An ebonite or plastic rod acquires a negative charge, if it is rubbed with wool. The piece of wool acquires an equal positive charge (B) Charging by electrostatic induction If a negatively charge rod is brought near the conductor mounted on insulated base as free electrons of conducting spheres close to rod experiences a force of repulsion and go to the other part of the sphere as shown in fig a .
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Consequently the part of sphere close to rod becomes positively charge due to deficiency of electrons in that region. As shown in figure b when the sphere is connected to the earth through a conducting wire, the some of the electrons of the spheres will flow to the ground. As shown in figure c, even if the connection with the earth is removed, the sphere retains the positive charge. When the negatively charged rod is moved away from the sphere, the electrons get redistributed on the sphere such that the same positive charge is spread all over the surface of the sphere as shown in figure d Important points regarding electrostatic induction (a) Inducing body neither gains nor loses charges (b) The nature of induced charge is always opposite to that of inducing charge (c) Induced charge can be lesser or equal to inducing charge but it is never greater than the inducing charge (d) Induction takes place only in bodies (either conducting or non conducting) and not particles (C) Charging by conduction Let us consider two conductor, one charged and other uncharged. We bring the conductors in contact with each other. The charge under its own repulsion will spread over both the conductors. Thus the conductors will be charged with the same sign. If charged and uncharged conductors are of same size charge will be equally divided if separated after contact.
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Coulomb's law : " Two point charges repel or attract each other with force which is directly proportional to the product of the magnitude of their charges and inversely proportional to the square of the distance between them" Let 'r' be the distance between two point charges qi and q2 the according to Coulomb's Iq111q21 law F 2 Klq111q21 2 K is proportionality constant . The value of K depends on the medium in which two point charges are placed 1 for vacuum ( or air) In SI system K = 4TtEo The constant Eo (=8.85XIO 12 Nm2C 2) is called "permittivity" of the free space Value of K = 9X109 Permittivity of medium If medium between the charges is not a vacuum ( or air) then Iq111q21 1 2 4TtE E Where Er is called relative permittivitV' of medium , it is a dimension less quantity, it is also called as dielectric constant or specific inductive capacity Term E = €0 Er are called as " absolute permittivitV' or "permittivity" of the medium Coulomb's law in vector form Force is a vector quantity, so Coulomb's law can be represented in vector form as follow Let two charges ql and q2 are like charges ( both positive or both negative charges) Let rl and rz be the position vector s of the charge qi and q2 . Let r12 be the vector pointing to ql, then displacement vector r12 = rl r2 qi rl rl r2 — r2 x
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According to coulomb's law, force acting on charge ql due to charge q2 is kq1q2 12 (r12)2 12 Where r12 = Irr r21 is the distance between two charges and us the unit vector of r12 in direction from q2 to qi 12 12 12 IF; — F*21 kq1q2 h - r2 El -T21 kq1t12 —5 (1) (IG-ül)3 Above equation is valid for any sign of charge whether positive or negative If charges are unlike then force will be negative indicating attractive force , if F is positive force is repulsive . Force on q2 due to ql in vector form can be represented as kql% (ä-Fl) 12 If we take out negative sign common from rl —h from equation (1), then we get —(ä — F*l) . Now (F2 — F*l) is a vector pointing from charge qi to cu. Also (lh — (171 — äl)3 thus from equation (1) and equation (2) we get F21 = 12 Thus force of interaction between two bodies is equal and opposite Or Coulomb's law agree with Newton's Third Law Principle of super position According to the principle of super position, the force acting on one charge due to another is independent of the presence of other charges. So we can calculate the force separately for each pair of charges and then their vector sum or find the net force on any q 4 14 Cll C12 12 13 charge. The figure shows a charge qi interacting with other charges. Thus, to find the force on qi, we first calculate the forces exerted by each of the other charges, one at a time. The net force Fl on Cll is simply the vector sum Fl = F12 + F + F + 13 14 Where F12 is the force on the charge due to the q2 and so on
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letter parameter X, o, p Charge distribution Relative parameter Along a line On surface Force due to continuous charge distributions To find the force exerted by a continuous charge distribution on a point charge, we divide the charge into infinitesimal charge element. Each infinitesimal charge element is then considered as a point charge. The magnitude of the force dF exerted by the charge dq on the charge qo is given by 1 Idql Iqol 2 4TTEoEr Where r is the distance between dq and qo . The total force is then found by adding all the infinitesimal force element, which involves integral Each type of the charge distribution is described in table below by an appropriate Greek- dq = X dx dq = o dA X, charge per unit length Q is charge Lis length , charge per unit area Q/A Q is charge , A is area Sl unit C/m C/m2 C/m3 Charge on element dq = p dV Throughout volume p, charge per unit volume Q is charge Vis volume Note : charge distribution is continuous but may not be uniform thus charge distribution is function of position

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