Title 02.Electrostatic-Potential-and-Capacitance-f.pdf ✅

Physics Smart Booklet 1 2.Electrostatic Potential and Capacitance Physics Smart Booklet Theory + NCERT MCQs + Topic Wise Practice MCQs + NEET PYQs

Physics Smart Booklet 3 Electrostatic Potential and Capacitance Electrostatic Potential It is the potential energy possessed by a unit positive charge at the given point in an electric field and is measured by the amount of work done in moving a unit positive charge from infinity to the given point against the field. It is a scalar quantity and is measured in volt. r r V dW E.dr   − −   = = The electric potential (V) at a distance r from a charge q is given by 0 1 q V 4 r   =      . If U is the change in potential energy of a system on a charge q move through a distance the against an electric field E, then  = − U qEd . Electrostatic potential at a point is V = U q  The potential energy per unit positive charge at a point in an electric field is called the electric potential at that point. Potential due to a point charge = 0 1 q 4 r  Potential due to a charged spherical conductor is 0 Q 4 x =  where x is distance of the point from the center of charged sphere. For points on the surface or inside the conductor the potential is 0 Q 4 r =  • The work done in moving a charged particle from one point to another in an electrostatic field depends only on the initial and final points, but not on the path between the two points. In figure the work done per unit charge in moving from A to B along all the paths 1, 2, 3 and 4 are equal. i.e., W1 = W2 = W3 = W4 = W (say). The work done W = VA ~ VB. • Work done in moving a charge over a closed path in an electric field is zero. Electric field is a conservative field. • The electric potential at a point due to positive charges is positive and due to negative charges is negative. The net potential at a point is the algebraic sum of the potentials due to different charges. Electric potential is scalar additive. Only the potential difference between two points VA ~ VB has a definite value. But, the absolute values of VA and VB are arbitrary and they have no physical significance. Only potential difference between two points is physically meaningful. • The potential difference between two points is the work done in moving one coulomb of positive charge from one point to the other. It is measured in volt. • Electric potential at a point due to a short dipole is given by 2 2 0 0 q(2a)cos p r V 4 r 4 r   = =   , where p = electric dipole moment. Potential due to a charged spherical conductor Path independence of work done
Physics Smart Booklet 4 • Potential at a point due to a dipole on the axial line is inversely proportional to the square of the distance from the dipole. At large distances, 2 1 V r  , whereas, for a point charge, 1 V . r  ➢ Potential is maximum ( = 0 or  and cos  =  1), along the axis of the dipole. ➢ At any point on the equatorial line, potential is zero (Thus, equatorial line of a dipole is equipotential). • Electric potential due to a system of charges is given by i 0 i 1 q V 4 r =   . • For a continuous distribution of charge, 0 dQ V 4 r =   ➢ dQ dl =  , for linear distribution of charge. ➢ dQ dS = , for surface distribution of charge. ➢ dQ d = v , for volume distribution of charge. Equipotential surface An equipotential surface is a surface passing through points at the same electric potential. ➢ Equipotential surfaces around a point charge are concentric spherical surfaces. ➢ Equipotential surfaces around a charged cylinder or line of charge are concentric cylindrical surfaces. ➢ Equipotential surfaces due to a large charged plane are planes parallel to the surface. ➢ For a uniform spherical distribution of charges (like a spherical shell or a sphere), the equipotential outside the spheres are concentric spheres around the centre of distribution of charges. ➢ All the lines in a plane passing through the centre of a dipole and perpendicular to the axis of the dipole lie on an equipotential surface of zero potential. If the dipole lies along x-axis, the y-z plane (x = 0) is an equipotential surface with V = 0. ➢ Electric field lines are perpendicular to an equipotential surface and hence work done in moving a charge on an equipotential surface is zero. Potential energy • Potential energy of a system of two charges is given by 1 2 0 12 1 q q U 4 r =  • Potential energy of a system of three charges is given by 1 2 2 3 3 1 0 12 23 31 1 q q q q q q U 4 r r r     = + +         • Energy of a system of several point charges is given by i j ij i j i j 0 ij 1 q q U U 4 r      = =          Capacitors When a conductor is charged, the charge spreads on its surface. If the conductor is smooth, it retains the charge for considerable time. Thus, a conductor can be used to store charge. The ability of a conductor to store charge is called its capacitance. The capacitance of a conductor is defined as its ability to store charge and is measured by the ratio of the charge added to the conductor to the rise in its potential.