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1
8
.
MAGNETIC AND MECHANICAL EFFECTS OF ELECTRIC CURRENT
Maxwell’s right hand clasp Rule
If we imagine a current carrying conductor to be clasped with right hand such that the thumb indicates
the direction of electric current, then the direction in which th
e fingers encircle the conductor gives the
direction of the magnetic field lines.
Biot

Savart’s Law or laplace’s Rule
According to Biot

Savart’s law the magnetic field (dB) at a point P at a distance r from a conductor of
length dL carrying a current I is
given by
is proportional it constant. Hence
H m

1
is the
permeability of free space.
Magnetic Field at the Centre of a Circular Coil
If the current through the coil of n turn of ra
dius r is I then, the field at the centre of the coil is
The direction of B is perpendicular to the plane of the coil and its direction follows from right hand
clasp rule.
Field at a point on the axis of a circular coil carrying c
urrent
Magnetic moment of a current loop
When n is the number of turns in the loop carrying current I and A is the radius of the loop.
The direction of the magnetic moment is given by right hand clasp rule.
Magnetic Field at a Po
int due to a Current Carrying Straight Conductor
Case (1): let P be a point at the centre of infinitely long solenoid. Then
and
Case (2): Let P be a point at one end of infinitely l
ong solenoid. Then
and
The field is along the axis and will be towards the observer if the current is counter clockwise
Tangent Galvanometer
For a given coil
at a given place, the quantity contained within the square brackets is a constant. Hence,
we write
, where
And K is called reduction factor of tangent galvanometer.
Mechanical effect of electric current
1.
The f
orce on a moving charge in a magnetic field is
Maximum force,
when
.
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2.
Force on a current carrying conductor placed in a uniform magnetic field is
.
where I is the current in the conductor, B is the field strength, L is the length of the
conductor and
is the angle between the current element and the direction of the field. Maximum
force,
when
.
3.
The force between two parallel current carrying conductors is given by
.
Suspended coil galvanometer
The current through a moving coil (suspended type) galvanometer is given by
Where,
c=Cou
ple per unit twist of the suspension wire.
n= number of turns in the coil
A=area of the coil
B=magnetic field
=deflection of the coil, due to the current I
Multiple Choice Questions
1.
The strength of the magnetic field around a st
raight wire :
a.
Is same everywhere around the wire
b.
Obeys inverse square law
c.
Is directly proportional to the square of
the distance from the wire
d.
None of the above
2.
A current loop placed in a magnetic field behaves like a :
a.
Magnetic dipole
b.
Magnetic substan
ce
c.
Magnetic pole
d.
All are true
3.
A positive charge is moving upward in a magnetic field which is towards north. The particle will be
deflected towards :
a.
East
b.
West
c.
North
d.
South
4.
If in circular coil A of radius R, current i if flowing and in another coil. B o
f radius 2R a current 2i is
flowing, then the ratio of the magnetic fields B
A
and B
B
a produced by them will be :
a.
1
b.
2
c.
1/2
d.
4
5.
The time period of a charged particle undergoing a circular motion in a uniform magnetic field is
independent of its :
a.
Speed
b.
Mas
s
c.
Charge
d.
Magnetic induction
6.
If a current is passed through a spring then the spring will :
a.
Expand
b.
Compress
c.
Remain same
d.
None of these
7.
At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound
can emit :
a.
Ele
ctrons
b.
Protons
c.
He
2+
d.
Neutrons
8.
Two long conductors, separated by a distance d carry current I1 and I2 in the same direction. They exert
a force F on each other. Now the current in one of them is increased to two times and its direction is
reversed. The dist
ance is also increased to 3d. The new value of the force between them is :
a.

2F
b.
F/3
c.

2F/3
d.
–
F/3
9.
The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a
distance of 4 cm form the centre is 54
What will be its value at the centre of the loop ?
a.
b.
c.
d.
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10.
A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at t
he
center of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of
the coil will be :
a.
nB
b.
n
2
B
c.
2nB
d.
2n
2
B
11.
Two thin long, parallel wires separated by a distance
‘d’ carry a current of ‘i’ A in the same direction.
They will :
a.
Attract each other with a force of
b.
Repel each other with a force of
c.
Attract each other with a force of
d.
Repel each other with a force of
12.
A uniform e
lectric field and a uniform magnetic field are acting along the same direction in a certain
region. If an electron is projected along the direction of the fields with a certain velocity, then :
a.
Its velocity will decreases
b.
Its velocity will increases
c.
It w
ill turn towards right of direction of motion
d.
It will turn towards left of direction of motion
13.
A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a
magnetic field B. The time taken by the particle t
o complete one revolution is :
a.
b.
c.
d.
14.
The wire shown in the figure carries a current of 40 A. What is the magnetic field at P ? The radius of
the bent coil is 2 cm]
(see fig. 1)
a.
Zero
b.
0.94 mT
c.
1.88 mT
d.
0.47 mT
15.
The figure shows a coil radius 2 cm concentric with a coil of radius 7 cm. Each coil has 100 turns, with
a current of 5 A in the large coil. The current needed in the smaller coil to given the total magnetic fiel
d
at the centre equal to 2 mT is
(see fig. 2)
:
a.
1.44 A
b.
0.793 A
c.
2.88 A
d.
3.4 A
16.
The wire loop PQRS formed by jointing two semicircular wires of radii R
1
and R
2
carries a current I as
shown. The magnitude of magnetic induction at the center C is
(see fig. 3)
:
a.
b.
c.
d.
17.
In the given figure, net magnetic field at the point P is
(see fig. 4)
:
a.
Not calculated
b.
Zero
c.
Non

zero
d.
Infinity
18.
Three infinitely long conductors A, B and
C are carrying current as shown in the figure. The position of
the point lying in the straight line AC where magnetic field is zero, is in
(see fig. 5)
:
a.
Between B and C at a distance of 3.2 cm from B
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b.
Between B and A at a distance of 3.2 cm from A
c.
Between
B and C at a distance of 1.3 cm from B
d.
Between B and A at a distance of 1.3 cm form B
19.
Infinite number of straight wires each carrying current I are equally placed as shown in the figure.
Adjacent wires have current in opposite directions. Net magnetic fie
ld at point P is
(see fig. 6)
:
a.
b.
c.
d.
Zero
20.
A wire of sine

graph shape lies in x

y plane as shown in the figure. A constant and static magnetic field
having magnitud
e 2T exists perpendicular to x

y

plane. The magnitude of force on the wire PQ if a
current 1A goes form P to Q is equal to
(see fig. 7)
:
a.
20 N
b.
9.2 N
c.
8 N
d.
4.6 N
21.
A straight rod of mass m and length L is suspended from the figure. The spring stretched a dis
tance x0
due to the weight of the wire. The circuit has total resistance R. When the magnetic field perpendicular
to the plane of paper is switched on, springs are observed to extend further by the same distance. The
magnetic field strength is
(see fig. 8)
:
a.
b.
c.
d.
22.
The magnetic field B at the centre of a circular coil of radius r is
times that due to a long straight
wire at a distance r from it,
for equal currents. Figure here shows three cases: in all cases the circular
part has radius r and straight ones are infinitely long. For same current the magnetic field B at the centre
P in cases I,II , III have the ratio
(see fig. 9)
:
a.
b.
c.
d.
23.
If two point charges q of a sufficiently large mass move parallel to one another with the same non

relativistic velocity
(shown in the figure), the rat
io of the magnitude of the magnetic and electric
interaction forces between charges is
(see fig. 10)
:
a.
b.
c.
d.
24.
Two long parallel wires are placed on a smooth horizont
al table. They have equal and opposite charges.
Work required to increases the separation between wires from a to 2a if magnitude of charge per unit
length on them is
, will be :
a.
b.
c.
d.
25.
Two long straight parallel conductors are separated by a distance of 5 cm and carrying current 20 A.
What work per unit length of a conductor must be done to increases the separation between conductors
to 10 cm,
if the curr
ent flows in the same direction
?
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a.
8 x 10

5
log
e
2
b.
log
e
2
c.
10

7
log
e
2
d.
None of these
26.
If a charged particle is projected in a region of magnetic field, then :
a.
The speed of the charged particle continuously changes
b.
The magnetic force on the charge
d particle must be zero
c.
The speed of the charged particle remains constant
d.
The magnetic force on the charged particle must not be zero
27.
Two Charged particles each of mass m and charge q are projected in a uniform magnetic field B with
the same speed as such
planes of motion of particles are perpendicular to magnetic field B, then :
a.
They move on circular path of same radii
b.
THE magnetic force on them are same to each other
c.
The kinetic energies of particles are same to each other
d.
All of the above
28.
A particle of
mass m and charge Q moving with velocity
describe3s a circular path of radius R when
subjected to a uniform transverse
magnetic field of inductance B
. The work done by the field when the
particle completes on full circle is :
a.
b.
c.
Zero
d.
29.
If a charged particle of charge
and mass 5 g
is
moving with constant speed 5m/s in a uniform
magnetic field B on a curve x
2
+ y
2
= 25, where x and y in metre
. The value of magnetic field will be :
a.
1 T
b.
1kT along z

axis
c.
5 kT along the x

axis
d.
1 kT along any line in x

y plane
30.
A charged particle of mass ma and charge q is accelerated through a potential difference of V volt. It
enters a region of uniform magnetic
field which is directed perpendicular to the direction of motion of
the particle will move on a circular path of radius given by :
a.
b.
c.
d.
31.
A long straight
wire
carri
es a current Io. A particle havi
ng
a positive charge q and mass m kept at a
distance y form the wire is projected towards it with a speed v. At the minimum separation, magnitude
of velocity of the charged particle will be
(see fig. 11)
:
a.
Zero
b.
v
c.
Infinity
d.
No
ne of these
32.
A proton moving with a constant velocity passes through a region of space without any change in its
velocity. If E and B represent the electric and magnetic fields respectively this region of space may not
have :
a.
b.
c.
d.
33.
An equilateral triangular loop ACD of side carries a current I in the direction shown in figure. The loop
is shown in figure. The loop is kept in a uniform horizontal magnetic field
as shown in figure, net
force on the loop is
(see fig. 12)
:
a.
Zero
b.
c.
Perpendicular to paper inwards
d.
Perpendicular to paper outwards
34.
Four wires each of length 2 m are bent into four loops P,Q,R and S and then suspen
ded into uniform
magnetic field. Some current is passed in each loop. Which statement is
correct?
(see fig. 13)
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a.
Couple on loop P will be the highest
b.
Couple on loop Q will be the highest
c.
Couple on loop R will be the highest
d.
Couple on loop S will be the high
est
35.
Wires 1 and 2 carrying currents i
1
and i
2
respectively are inclined at an angle
to each other. What is
the force on a small element dl of wire 2 at a distance r from wire 1 (as shown in figure) due
to the
magnetic field of wire
1
?
(see fig. 14)
a.
b.
c.
d.
36.
A particle of charge
–
16 x 10

18
C moving with velocity 10 ms

1
along the x

axis enters a region where a
magnetic field of induction B is alon
g the y

axis and an electric field of magnitude 10
4
V/m is along the
negative z

axis. If the charged particle continues moving along the x

axis, the magnitude of B is :
a.
10
3
W
b
/m
2
b.
10
5
W
b
/m
2
c.
10
16
W
b
/m
2
d.
10

3
W
b
/m
2
37.
A current i ampere flows along an infinite
ly long straight thin walled tube, Then the magnetic
induction at any point inside the tube is :
a.
Infinite
b.
Zero
c.
d.
38.
Two concentric coils each of radius equal to
cm are placed at right an
gles to each other, 3A and 4A
are the current following in each coil respectively. The magnetic induction in W
b
/m
2
at the centre of the
coils will be
:
a.
12 x 10

8
b.
10

5
c.
5 x 10

5
d.
7 x 10

5
39.
In a region, steady and uniform electric and
magnetic fields are present. These two fields are parallel to
each other. A charged particle is released from rest in this region. The path of the particle will be a :
a.
Helix
b.
Straight line
c.
Ellipse
d.
Circle
Answers
Q
A
Q
A
Q
A
Q
A
Q
A
Q
A
Q
A
Q
A
Q
A
Q
A
1
A
2
A
3
A
4
A
5
A
6
B
7
A
8
C
9
A
10
B
11
A
12
A
13
D
14
B
15
B
16
B
17
B
18
A
19
A
20
C
21
B
22
A
23
D
24
D
25
A
26
C
27
D
28
C
29
B
30
C
31
B
32
C
33
D
34
D
35
C
36
A
37
B
38
C
39
B
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An educational Teleserial In Doordarshana Chandana
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IIT

JEE, AIEEE
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CET
.
# 157, 6
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–
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23376200, 25991124
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1, 2,
3, 4, 5
6
7
8
9)
10)
11)
12)
13
)
14)
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