Magnetic Effects of Current and Magnetism Notes and MCQs

Notes 65 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Yash Kuruvilla

108
SUMMARY
Important tips of each topic
1. Biot-Savart;s law :
0
2
0
2
ˆ
µ 1 dl × r
dB =
4π r
In Vaccum or AIR
µ 1 dl sinθ
dB =
4π r









r 0
2
r 0
2
ˆ
µ µ 1 dl × r
dB =
4π r
In any Medium
µ µ 1 dl sinθ
dB =
4π r









2. For a WIRE
(A) Finite length of a wire
 
0
1 2
sin sin
4

   

I
B
d
 
0
1 2
cos cos
4

   

I
d
(B) Infinite length of a wire
o
21
o
21
0OR90 
 
0
I
1 1
4 d

 

B
 
0 0
I I
2
4 d 2 d
 

 
(C) Semi - infinite length of a wire
o
2
o
1
90;0 
 
0
1
0 1
4 d

 

B
0
1
4 d



Page 1
109
3. For a RING :
(A) For N = 1 turn
 
2
0
3
2 2
2
µ I a
B =
2 a + x
(B) For N = N turns
 
2
0
3
2 2
2
µ I a
B = N
2 a + x
 
 
 
 
 
(C) At the centre (x = 0)
0
I
B N
2a

 

 
 
(D) At x >> a
0
3
µ 2M
B =
4π x
[Just as, mag. field on the axis of a Bar-magnet]
Where m = magnetic moment
4. For Solenoid
(A) Finite length solenoid
 
0
µ nI
B = sin α + sin β
2


N
nWhere 
Where
 and
are angles mode at the either end of the solenoids.
n = no. of turns per unit length ; N = total no. of turns.
(B) Infinite length solenoid
o
90
 
0
µ nI
B = 1 + 1
2
0
B = µ nI

N
nWhere 
(C) Mag. field at either end
o
90and0 
 
0
µ nI
Bend Point = 0 + 1
2
Page 2
110
0
1
nI
2
 
Binside
2
1
Bend 
(D) Toroid
0
µ
I
B = N
2π r
 
 
 
5. Force on a charged particle in magnetic field.
(A)


BVqF 
 sinBVqF
Direction of force can be determine by using
(B) Fleming's Left and rule
First finger indicates

direction of magnetic field.
Middle finger indicates

direction of motion of POSITIVE charge particle
Thumb indicates

direction of force
(C)
oo
180or0If 
charged particle moves on straight line.
(D)
BVqFBVie90If
o

charged particle moves on circular path of radius r
q
mV2
B
1
qB
mK2
qB
p
qB
mv
r 
(E) If

is neither zero nor perpendicular it performs Helical path.
 radius of helical path


qB
sinVm
r


 periodic time
2π m
T =
qB
 pitch of the helix
 





tan
r2
qB
cosm2
cosT
 No. of pitches
cetandisPitch


Page 3
111
6. Lorentz's force


F = q E + V × B
 
 
   
7. Cyclotorn
Frequency
1
2
 

Bq
f
T m
8. Force between two parallel current carrying wires.
0 1 2
µ I I
F =
2π Y

0 1 2
µF I I
=
2π Y
Case (i) If I
1
and I
2
are flowing in same direction Attraction.
Case (ii) If I
1
and I
2
are flowing in opposite direction Repulsion.
9. Torque acting on a rectangle frame
 sinBINA
(i) If frame is parallel to the field
o
0

0
(ii) If frame is perpendicular to the field
o
90

BINA
10. Moving coil Galvano meter.
(i)
BINA
 Krestoning Where
deflection in galvanometer
 KBINA
K
I
BNA
 
 
 
 
(ii) Current sensitivity (S
I
) :
The deflection produced in the Galvanometer per unit current flowing throught it.
I
BNA
S
I K

 
(iii) Voltage sensitivity (S
V
) :
The deflection produced in the Galvanometer per unit voltage applied to it.
KR
BNA
R
SI
IRV
S
V





I
1
I
2
y
Page 4
112
11. Bar magnet and its pole strength (m)
Pole strength :
 The strength of a magnetic pole to atiract magnetic material towards itself.
 Unit is
 
Newton
Amp meter
Tesla
 Pole strength of the magnet depends on the nature of material of magnet and area of
cross- section.
 m does not depend upon length.
12. Magnetic dipole moment (M) :


2mM 
 dir
-n
is from south pole to North pole
 unit is
Tesla
meterNewton
meterAmp
2


13. Cutting of a rectangular bar-magnet.
If a bar-magnet of length L and breadth b is cut into n equal parts then
(i) Length of each part
n
L
L 

(ii) Breadth of each part
n
b
b 

(iii) Mass of each part
n
w
w 

(iv) Pole-strength (m) of each part
n
m
m 

(v) Magnetic moment (M) of each part
n
M
M 

(vi) Initial (Original) moment of inertia of a bar


22
bLW
12
1
I 
(vii) After cutting new moment of inertia
2
n
I
I 

Page 5
113
14. Cutting of a thin bar-magnet for thin bar magnet b = 0
2
L w m I
L ; w ; m ; I
n n n n
   
   
15. Magnetic field and Magnetic flux :
(i) Magnetic field is denoted by B and its units are
2 2 2
.
   
 
Weber Newton Joule Volt see
Tesla
m Amp meter Amp m m
(G) unit is Gauss 1 Tesla = 10
4
Gauss
16. Magnetic permeability
 
:  
o
Absolute permeability of air or vaccum
Amp
metertesla
104
7



typermeabilirelative
r

r
0 0
µ B mag. Flux density in material
µ = = =
µ B mag. Flux density in vaccum
17. Intansity of magnetising field (H
-1
) :
It is the degree or extent to which a magnetic field can magnetise a substance.


B
H
meter
Ampere
unit 
wbm
J
teslam
J
wb
N
teslam
N
m
A
32






CGS unit : Oersted
meter
Amp80
Oersted1 
18. Intensity of magnetisation (I)
(i) It is the degree to which a substance is magnetised when placed in a magnetic field.
(ii) It is also defined as the pole strength per unit cross-sectional area of the substance.
(iii) It is also defined as Induced dipole moment per unit volume.
Volume
M
A
m
I 
meter
Ampere
isunit
Page 6
114
19. Magnetic susceptibility
 
m

and permeability
o m
B = B + B
0 0
= µ H + µ 1


0
= µ H + I


0 m
B = μ H 1 + χ
mr
1 
20. Coulomb's law in magnetism.
2
21
r
mmK
F 
where m
1
, m
2
= pole strength
where
7
0
K 10
4


 

in SI unit
= 1 in CGS unit
21. Magnetic field due to bar-magnet
(i) On axis of a bar-magnet
0
3
2M
B axis
4 r



(ii) On equator of a bar-magnet
0
3
M
Bequator
4 r



22. Bar-magnet in magnetic field.
(i) Torque
 sinMB
(ii) Work
 
21
coscosMBW 
(iii) Potential energy
 cosMBBMU
23. Tangent Galvanometer :
In equilibrium
 tanBB
H
Where
0
nI
B
2r


n = no. of turns
r = radius of the coil
I = Current to be measured
 = angle made by needle from the direction of B
H
in equilibrium.
Page 7
115
24. Deflection magnetometer :
It works on principle of tangent law
(i) A-Position :
The magnetometer is set perpendicular to magnetic meridian so that magnetic field due
to magnet is in AXIAL position.
0
H
3
2M
B B tan
4 r

  

(ii) B-position :
The arms of magneto meter are set in magnetic meridian so that the magnetic field due
to magnet is at its equatorial position.
H
3
M
B B tan
4 r

  

(iii) Comparison :
2
1
2
1
tan
tan
M
M



3
2
1
r
r









25. Vibration Magnetometer :
Periodic time
H
I
T 2
MB
 
2
H
2
TB
I4
M



(i) Comparison of horizontal components of earth's magnetic field at two places.
H
I
T 2
MB
 
but I and M are constant


 
2
1
2
2
2
H
1
H
H
2
T
T
B
B
B
1
T 
Page 8
116
(ii) Comparison of magnetic moment of two magnets of same size and mass
H
MB
1
2T 
but I and B
H
are constant.
2
1
2
2
2
1
2
T
T
M
M
M
1
T 
26. Diamagnetic material :
 magnetic dipole moment M = 0
 experience fore towards weak mag. field.
 magnetic susceptibility
.Ve
m

27. Paramagnetic material :
magnetic dipole moment = M = 0
experience force towrards strong mag. field.
magnetic susceptibility
m
Ve.  
28. Curie Law :
T
1

T
C

29. Curie - weiss law :
At temperature above curie temperature the magnetic susceptibility of force magnetic material
is inversely proportional to


C
TT 
C
TT
1


C
TT
C


Page 9
117
MCQ
For the answer of the following questions choose the correct alternative from among
the given ones.
1.
An element
 dxd
(where dx = 1 cm) is placed at the origin and carries a large current I
= 10 Amp. What is the mag. field on the Y-axis at a distance of 0.5 meter ?
(a)
Tk
ˆ
102
8

(b)
Tk
ˆ
104
8

(c)
Tk
ˆ
102
8

(d)
Tk
ˆ
104
8

2. Two straight long conductors AOB and COD are perpendicular to each other and carry currents I
1
and I
2
. The magnitude of the mag. field at a point "P" at a distance "a" from the point "O" in a
direction perpendicular to the plane ABCD is
(a)
 
0
1 2
I I
2 a



(b)
 
0
1 2
I I
2 a



(c)
 
1
2 2
0
2
1 2
I I
2 a



(d)
 
0 1 2
1 2
I I
2 a I I

 
3. B

R graph. The mag. field B at a distance r from a long straight wire carrying a current varies with
r as shown in Fig.
(a) (b)
(c) (d)
4. A current path shaped as shown in figure produces a mag. field
at point "P", the centre of the arc BC. If the arc subtends an
angle of 30
0
and the radius of the arc is 0.6 meter. What is the
magnitude of the field at point P if the current is 3 AMP ?
(a)
T1062.2
6

(b)
T1062.2
7

(c)
T1062.3
7

(d)
T1062.2
8

Page 10

Magnetic Effects of Current and Magnetism Notes and MCQs

Magnetic Effects of Current and Magnetism Notes and MCQs

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