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Transcript
Happy New Year -2006 Champak Baran Das Physics Group (3242-S) [email protected] Chamber Consultation: Friday 5.00 to 6.00 PM PHYSICS-II (PHY C132) Text Book: PHYSICS, VOL 2: by Halliday, Resnick & Krane (5th Edition) Reference Books: Introduction to Electrodynamics: by David J. Griffiths (3rd Ed.) Concepts of Modern Physics: by A. Beiser (6th Ed.) Electromagnetism deals with electromagnetic force and field Electromagnetism Electricity Magnetism Optics Electric Field • An electric field is said to exist in the region of space around a charged object. • When another charge object enters this electric field, an electric force acts on it. The test charge qo experiences an electric field E directed as shown. The electric field E at a point in space is defined as the electric force F acting on a unit positive test charge qo placed at that point : F E = lim q0 0 q0 Test charge should be small not to disturb the charge distribution of the source (a) For small enough qo, the distribution is undisturbed. (b) For a larger qo' , the distribution gets disturbed. Electric force and field r q1 + q0 The Coulomb force is F= kq1q0/r2 (where, k = 1/40) The electric field at r = Force per unit charge , => E = F/q0 = kq1/r2 Positive source charge q1 E E= kq1/r2 Negative source charge q1 E Negative source charge Electric Field Lines Electric Field Lines: a graphic concept as an aid to visualize the behavior of electric field. •Begin on + charges and end on - charges. •Number of lines entering or leaving a charge is proportional to the charge Electric Field Lines: (contd.) •Density of lines indicates the strength of E at that point •The tangent to the line passing through any point in space gives the direction of E at that point •Two field lines can never cross. Electric Field Lines Like charges (++) Opposite charges (+ -) . Electric Dipole An electric charge dipole consists of a pair of equal and opposite point charges separated by a small distance, d. -Q +Q d Dipole Moment Dipole moment p is a measure of the strength of the dipole and indicates its direction p Qd +Q dd -Q p is in the direction from the negative point charge to the positive point charge. Electric Field of a dipole To find the electric field E at point P, At P, the fields E1 and E2 due to the two charges, are equal in magnitude. The total field is E = E1 + E2, E1 = E2 = kq/r2 = kq /(y2 +a2) The y components cancel, and x components add up => E || x-axis |E| = 2E1 cos . cos = a/r = a/(y2 +a2)1/2 E = k 2aq /(y2 +a2)3/2 Electric Field of a dipole (cont’d) E = k 2aq /(y2 +a2)3/2 If y >> a, then E ~ k p/y3 E due to a dipole ~ 1/ r3 E due to a point charge ~ 1/ r2 Electric Field of a dipole (cont’d) y q -q To find the electric field at a distant point along x the x-axis. 2a The E field at any point x : kq kq 2k (2aq) x E ( x a) 2 ( x a) 2 ( x 2 a 2 ) 2 When x >>> a, then x2 a2 ~ x2 E ~ 4kqa/x3 Ex 26.11: Field due to Electric Quadrupole 2 3 2qa E 4 2 0 x Pr 26.4: Field due to Electric Quadrupole To find out E at P: 2 3 2qd E 4 4 0 z A Dipole in Electric field The net force on the dipole is always zero. But there is a finite torque acting on it This torque tends to rotate it, so that p lines up with E. Dipole in a Uniform Electric Field x tpxE Torque about the com t F x sin F(d-x)sin Fdsin qEdsin pEsin pxE Work done by external field E to rotate the dipole through an angle 0 to : W t .d 0 0 0 t d pE sin d pE cos cos 0 Change in potential energy of the system: U W pE (cos cos 0 ) Choosing reference angle 0 = 90° and U(0 ) = 0. U pE cos p E Ex 26.36: • Dipole: q = 1.48 nC; d = 6.23 µm • E (ext.) = 1100 N/C To find: (a) dipole moment p (b) difference in potential energy corresponding to dipole moment parallel and antiparallel to E. Ans. (a) p = 9.22 ×10-15 Cm (b) U = 2.03×10-11J Ex 26.37: Dipole: q = 2e; d = 0.78 nm E (ext.) = 3.4 ×106 N/C. To find: torque t (a) p E (b) p E (c) p is opposite to E