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Happy New Year -2006
Champak Baran DasPhysics 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
Electromagnetism deals with electromagnetic force and
field
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.
E = lim q0q0 0
F
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 :
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
The electric field at r = Force per unit charge ,
=> E = F/q0 = kq1/r2
+ q0q1
r
The Coulomb force is F= kq1q0/r2
(where, k = 1/40)
Negative source charge
E= kq1/r2
Positive source charge
q1
E
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 DipoleElectric DipoleAn An electric charge dipole consists consists of a pair of equal and opposite point of a pair of equal and opposite point charges separated by a small charges separated by a small distance, distance, d.d.
d
+Q -Q
Dipole Moment Dipole moment p is a measure of the strength of the dipole and indicates its direction
+Q
-Q
d p is in the direction from the negative point charge to the positive point charge.
d
dQp
Electric Field of a dipoleTo 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,
E = k 2aq /(y2 +a2)3/2
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
Electric Field of a dipole (cont’d)
If y >> a, then E ~ k p/y3
E due to a dipole ~ 1/ r3
E due to a point charge ~ 1/ r2
E = k 2aq /(y2 +a2)3/2
Electric Field of a dipole (cont’d)
2a
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
22222 )(
)2(2
)()( ax
xaqk
ax
kq
ax
kqE
Ex 26.11: Field due to Electric Quadrupole
4
0
2
2
23
x
qaE
Pr 26.4: Field due to Electric Quadrupole
To find out E at P:
4
0
2
4
23
z
qdE
A Dipole in Electric field
The net force on the dipole is always zero.
This torque tends to rotate it, so that p lines up with E.
But there is a finitetorque acting on it
p x E
Dipole in a Uniform Electric Field
Torque about the com F x sin F(d-x)sin Fdsin qEdsin pEsin p x E
x
Work done by external field E to rotate the dipole through an angle 0 to :
0
.
dW
0
00
coscos
sin
pE
dpEd
Change in potential energy of the system:
)cos(cos 0 pEWU
Choosing reference angle 0 = 90°
and U(0 ) = 0.
EppEU
cos
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
(a) p E
(b) p E
(c) p is opposite to E