Transcript PHYSICS-II (PHY C132)

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Champak Baran Das
Physics Group (3242-S)
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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.)
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 = 1/40)
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
tpxE
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