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**Happy New Year -2006 Champak Baran Das**

Physics Group (3242-S) Chamber Consultation: Friday 5.00 to 6.00 PM

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**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.)

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**Electromagnetism deals with electromagnetic force and field**

Optics Electricity Magnetism

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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.

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**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 : E = lim q0 q0 0 F

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**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.

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**Electric force and field**

+ q0 q1 r 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

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**Negative source charge**

q1 E Positive source charge E= kq1/r2 q1 E Negative source charge

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**Negative source charge**

Electric Field Lines

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**Begin 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

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**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.

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Electric Field Lines Like charges (++) Opposite charges (+ -) .

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Electric Dipole An electric charge dipole consists of a pair of equal and opposite point charges separated by a small distance, d. d +Q -Q

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**Dipole Moment d Dipole moment p is a measure of the strength**

of the dipole and indicates its direction +Q -Q p is in the direction from the negative point charge to the positive point charge. d

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**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

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**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

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**Electric Field of a dipole (cont’d)**

q -q x y To 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

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**Ex 26.11: Field due to Electric Quadrupole**

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**Pr 26.4: Field due to Electric Quadrupole**

To find out E at P:

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**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.

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**Dipole 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 E x t = p x E

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**Work done by external field E to rotate the dipole through an angle 0 to :**

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**Choosing reference angle 0 = 90°**

Change in potential energy of the system: Choosing reference angle 0 = 90° and U(0 ) = 0.

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**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

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**Ex 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

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