The flux - DelE Directorate of Education

1 1 XII PhysicsElectric charges, Conversation of charges, Coulomb s Law; Force between two pointscharges, forces between multiple charges, Superposition charge field , electric field due to a point charge electric field lines, electric dipole, electric field due to dipole; torque on a dipole in uniform electric flux, statement of Gauss Theorem and its applications to find field due to infinitelylong straight wire, uniformly charged infinite plane sheet and uniformly charged thinspherical shell ( field inside and outside)

2 electric Potential, Potential difference, electric potential due to a point charge, a dipoleand system of charges, equipotential surfaces, electrical potential energy of a system oftwo point charges and of electric dipole in an electrostatic and Insulators, free charges and bound charges inside a conductor, Dielectricand electric polarization, Capacitors and Capacitance, combination of capacitances inseries and of a parallel plate capacitor with or without dielectirc medium between theplates energy stored in a capacitor, Van de Graff s Law.

3 The mutual electrostatic force between two point charges q1 and q2 is proportional tothe product q1 q2 and inversely proportional to the square of the distance r separating 1 221122q qForce on q due to q krr 12r is a unit vector in the direction from q1 to q2 and k is constant of 201k9 10 N m c4 2 XII PhysicsElectric field of an electric dipole at equitorial point at a distance r from the centre :2 p4 r 03~~for >> r aE =2 p r( )r a3/22214 0+at axial pointp4 r03~~for >> r aE =p( )

4 R a3 /22214 0 at equitorial pointThus note 1/r3 dependence of dipole electric field in contrast to 1/r2 dependence of electric field due topoint electric field due to a thin spherical shell of uniform surface charge density is 20qEr r R2 r E 0 r Rwhere r is the distance of the point from the centre of the shell and R the radius of the shell, q is totalcharge of the flux of electric field E through a small area element S is given by : = E. s s = s nWhere s is the magnitude of area element and n is unit vector normal to the area element which canbe considered plane as s is electric field E due to thin.

5 Infinitely long straight wire of uniform linear charge density isE = 2 r 0nwhere r is the perpendicular distance of the point from the wire and n is the radial unit vector in the planenormal to the wire passing through the electric field due to an infinite thin plane sheet of uniform surface charge density isE = 2 0nwhere n is a unit vector normal to the plane, outward on either PhysicsIn a uniform electric field E, an electric dipole experiences a tongue given by = p E, but no netforce is dimensions of (i) electric field are MLT 3 A 1 (ii) electric flux are ML3 T 3 A potential at a point represented by position vector r due to a point charge Q placed at the originis given by :04 r QVwhere r rElectric potential at a point represented by position vector r due to a dipole of dipole moment p at theorigin isV =p cos 2 ( a cos ) 0r222=4 0r2p.

6 Rfor r >> aHere = angle between p and potential energy of a pair of point charges q1 and q2 at a separation r is1 20q r The potential energy of a dipole of dipole moment p in a uniform electric field E isU = p . ETorque experienced by an electric dipole in a uniform electrostatic field is p E. An electric dipole mustexperience zero torque and its potential energy should be(i)Minimum for stable equilibrium.(ii)Maximum for unstable field is zero in the interior of a conductor due to charges on the surface of the conductoror outside the the case of a charged conductor E = 0n where n is a unit vector along the outward normal to theconductor and is the surface charge charge given to a hollow or a solid conductor will always appear on its outer of an air filled parallel plate capacitor 4 XII PhysicsThe capacitance of a capacitor with a dielectric medium completely filling the space between the platesis K times its

7 Capacitance without the dielectric. Here K is the dielectric constant of the a series combination of capacitors connected across a dc source, charge on each capacitor will bethe same. From here we gets1231 1 1 C C C For a parallel combination of capacitors, connected across a dc source, potential difference (or voltage)across each capacitor will be the same. From here we getCp = C1 + C2 + C3 + ..Energy stored in a charged capacitor is given by 221Q 1 UCVQV22C 2 and energy density for aparallel plate capacitor is 201E.

8 2 schematically an equipotential surface of a uniform electrostatic field along X field lines due to (i) two equal positive charges near each other (ii) a the physical quantity whose SI unit is volt/meter. Is it a scalar or a vector quantity? point charges repel each other with a force F when placed in water of dielectric constant will the force between them when placed the same distance apart in air? uncharged conductor A placed on an indulsting stand is brought near a charged insulatedconductor B. What happens to the charge and potential of B?

9 Point charge Q is placed point O shown in Fig. Is the potential difference VA VB positive,negative or zero, if Q is (i) positive (ii) negative dipole moment of CuSO4 molecule is 10 32 Cm. Find the separation between copperand sulphate capacitance of three identical capacitors connected in parallel is 12 microfarad. What will bethe net capacitance when two of them are connected in (i) parallel (ii) series? electron and proton are released from rest in a uniform electrostatic field . Which of them willhave larger acceleration?

10 Charge q is placed at the centre of an imaginary spherical surface. What will be the electric fluxdue to this charge through any half of the an uniform electric field of strength E, a charged particle Q moves point A to point B in thedirection of the field and back from B to A. Calculate the ratio of the work done by the electricfield in taking the charge particle from A to B and from B to the electric field vs distance (from the centre) graph for (i) a long charged rod with linearcharge density < 0 (ii) spherical shell of radius R and charge Q > represent the position of a dipole in (i) stable (ii) unstable equilibrium whenplaced in a uniform electric charge Q is distributed over a metal sphere of radius R.