Presentation on theme: "Happy New Year Champak Baran Das"— Presentation transcript:
1Happy New Year -2006 Champak Baran Das Physics Group (3242-S)Chamber Consultation: Friday 5.00 to 6.00 PM
2PHYSICS-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.)
3Electromagnetism deals with electromagnetic force and field OpticsElectricityMagnetism
4Electric FieldAn 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.
5The 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 :E = limq0q0 0F
6Test 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.
7Electric force and field + q0q1rThe Coulomb force is F= kq1q0/r2(where, k = 1/40)The electric field at r= Force per unit charge ,=> E = F/q0= kq1/r2
10Begin on + charges and end on - charges. 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
11Electric Field Lines: (contd.) Density of lines indicates the strength of E at that pointThe tangent to the line passing through any point in space gives the direction of E at that pointTwo field lines can never cross.
12Electric Field LinesLike charges (++)Opposite charges (+ -).
13Electric DipoleAn electric charge dipole consists of a pair of equal and opposite point charges separated by a small distance, d.d+Q-Q
14Dipole Moment d Dipole moment p is a measure of the strength of the dipole and indicates its direction+Q-Qp is in the direction from the negative point charge to the positive point charge.d
15Electric 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)1/2E = k 2aq /(y2 +a2)3/2
16Electric Field of a dipole (cont’d) E = k 2aq /(y2 +a2)3/2If y >> a, then E ~ k p/y3E due to a dipole ~ 1/ r3E due to a point charge ~ 1/ r2
17Electric Field of a dipole (cont’d) q-qxyTo find the electric field at a distant point along the x-axis.The E field at any point x :When x >>> a, then x2 a2 ~ x2 E ~ 4kqa/x3
19Pr 26.4: Field due to Electric Quadrupole To find out E at P:
20A Dipole in Electric field The net force on the dipole is always zero.But there is a finitetorque acting on itThis torque tends to rotate it,so that p lines up with E.
21Dipole in a Uniform Electric Field Torque about the com = t= F x sin q + F(d-x)sin q= Fdsin q= qEdsin q= pEsin q= p x Ext = p x E
22Work done by external field E to rotate the dipole through an angle 0 to :
23Choosing reference angle 0 = 90° Change in potential energy of the system:Choosing reference angle 0 = 90°and U(0 ) = 0.
24Ex 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
25Ex 26.37: Dipole: q = 2e; d = 0.78 nm E (ext.) = 3.4 ×106 N/C. To find: torque (a) p E(b) p E(c) p is opposite to E