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10. Magnetic field due
to electric current
INTRODUCTION
Iron Pieces
5. Magnetic Field Along Centre And Axis Of Circular Loop
MAGNETIC FORCE 1
Magnetic force 2
Your upright
thumb shows the
direction of the
magnetic force on
a positive particle.
Point your fingers
in the direction of
๐’— and the curl
them toward the
direction of ๐‘ฉ.
EXAMPLES BASED
ON MOTION OF
CAHRGEDPARTICLE
CYCLOTRON
(PRINCIPLE,CONSTRUCTION
AND WORKING
RADIUS AND PERIOD
OF POSITION ION
MCQS ON ELECTRON - 1
MCQS ON ELECTRON - 1
CHARGED PARTICLE
MOVING IN A MAGNETIC
FIELD
qVB=
๐ฆ๐•๐Ÿ
๐ซ
qB=
๐ฆ๐•
๐ซ
๐’“ =
๐’Ž๐’—
๐’’๐‘ฉ
T =
๐Ÿ๐›‘๐ซ
๐•
T =
๐Ÿ๐›‘๐ฆ๐•
๐•๐ช๐
T =
๐Ÿ๐›‘๐ฆ
๐ช๐
Time period (T),
frequency (f)and
angular frequency (๐›š)
are independent of
velocity of the charge.
f =
๐Ÿ
๐‘ป
f =
๐ช๐‘ฉ
๐Ÿ๐…๐’Ž
Angular frequency
๐Ž =2๐…f =2๐…
๐ช๐‘ฉ
๐Ÿ๐…๐’Ž
๐Ž =
๐ช๐‘ฉ
๐’Ž
FORCE ACTING ON A CONDUCTOR
CARRYING CURRENT IN A
MAGNETIC FIELD
FORCE ON A CLOSED
CIRCUIT IN A
MAGNETIC FIELD
Magnetic force on a Wire Carrying a current
F = I(L x B)
dF = I(dL x B)
F = โˆฎ ๐๐… = Iโˆฎ ๐’…๐‘ณ x B
CASE 1 : Straight wire
CASE 2 : Wire of any arbitrary wire
F = Iโˆฎ ๐๐ฅ x B
TORQUE ON A CURRENT
LOOP IN MAGNETIC
FIELD - 1
TORQUE ON A CURRENT
LOOP IN MAGNETIC
FIELD - 2
TORQUE ON A CURRENT
LOOP IN MAGNETIC
FIELD - 3
INTRODUCTION TO GALVANOMETER
AND PRINCIPLE, CONSTRUCTION OF
GALVANOMETER
WORKING OF MOVING
GALVANOMETER
MCQS ON
GALVANOMETER - 1
MCQS ON
GALVANOMETER - 2
SENSITIVITY AND ACCURACY
OF MOVING COIL
GALVANOMETER
MCQ ON SENSITIVITY
Q. A coil of moving coil galvanometer has 100 turns and effective area 0.05๐’Ž๐Ÿ .
It is suspended in a radial magnetic field of induction 0.01 Wb/๐’Ž๐Ÿ. The
torque per unit twist of the suspension fibre is 5 ร— ๐Ÿ๐ŸŽโˆ’๐Ÿ— Nm/degree. What is
the current sensitivity of the moving coil galvanometer?
a) ๐Ÿ๐ŸŽ๐Ÿ“
degree/ampere b)๐Ÿ๐ŸŽ๐Ÿ•
degree/ampere
c) 2ร—๐Ÿ๐ŸŽ๐Ÿ” degree/ampere d)3ร— ๐Ÿ๐ŸŽ๐Ÿ“ degree/ampere
MAGNETIC DIPOLE
MOMENT
The magnetic field
pattern produced by
a small current loop
is similar to magnet
EXAMPLES:
MAGNETIC DIPOLE
MOMENT
(Will be out of the plane)
By right hand rule.
MAGNETIC DIPOLE FOR A
POTENTIAL ENERGY
MAGNETIC POTENTIAL ENERGY FOR A DIPOLE
Work done,
๐›• = ๐ฆ๐ ๐ฌ๐ข๐ง๐›‰
PE = โˆซ ๐…
ds
๐›• d๐œฝ
๐œƒ1
๐œƒ2
๐œ ๐‘‘๐›ณ
=
โˆซ
๐œฝ๐Ÿ
๐œฝ๐Ÿ
๐’ŽBsin๐œฝ ๐’…๐œฝ mBโˆซ
๐œฝ๐Ÿ
๐œฝ๐Ÿ
๐’”๐’Š๐’๐œฝ ๐’…๐œฝ mB(โˆ’cos๐œฝ)๐œฝ๐Ÿ
๐œฝ๐Ÿ
= = =
U = -mb(cos๐œฝ๐Ÿ.cos๐œฝ๐Ÿ)
U = -mb(cos๐œฝ๐Ÿ.cos๐œฝ๐Ÿ)
U = -mb(cos๐œฝ๐Ÿ.cos๐œฝ๐Ÿ)
๐œฝ๐Ÿ= ๐Ÿ—๐ŸŽยฐ ๐œฝ๐Ÿ = 0
U = -mB cos๐œฝ
U = -mB cos๐œฝ
Case 1 : ๐œฝ = ๐ŸŽ
Case 2 : ๐œฝ = ๐Ÿ—๐ŸŽ
Case 3 : ๐œฝ = ๐Ÿ๐Ÿ–๐ŸŽ
U = -mB cos๐ŸŽ
U = -mB cos๐Ÿ—๐ŸŽ
U = -mB cos๐Ÿ๐Ÿ–๐ŸŽ
U = -mB
U = 0
U = mB
MIN MAX
BIO โ€“ SAVARTโ€™S LAW- I
BIO โ€“ SAVARTโ€™S LAW- II
FORCE BETWEEN TWO INFINITELY
LONG CURRENT CARRYINGB
PARALLEL CONDUCTORS - I
FORCE BETWEEN TWO INFINITELY
LONG CURRENT CARRYINGB
PARALLEL CONDUCTORS - II
MAGNETIC FIELD DUE TO A
CIRCULAR ARC
EXAMPLES BASED ON
CIRCUALR ARC 1
MAGNETIC INDUCTION AT A POINT
ALONG THE AXIS OF A COIL
CARRYING CURRENT - I
(1)
(2)
(2)
MAGNETIC INDUCTION AT A POINT
ALONG THE AXIS OFA COIL
CARRYING CURRENT - II
From โˆ†๐€๐Ž๐, ๐ฌ๐ข๐ง๐›‚ =
๐š
๐ซ
Now,โˆซ ๐๐ฅ = ๐Ÿ๐›‘๐š = ๐ญ๐จ๐ญ๐š๐ฅ ๐ฅ๐ž๐ง๐ ๐ญ๐ก ๐จ๐Ÿ ๐ฅ๐จ๐จ๐ฉ
(3)
(3)
Hence,
(4)
(4)
(5)
When point P lies far away from the center of coil (loop) then x >>> ๐’‚,
Note
In each case, magnetic induction is directed along
the axis of the coil and perpendicular to the plane of
MAGNETIC LINES FOR CURRENT
LOOP
Magnetic Lines for a Current Loop:
We know that the magnetic field at a point P on the axis is
given by Eq. (10.53) as
๐ต๐‘ง =
๐œ‡0๐ผ๐‘…2
2 z2 + ๐‘…2 3/2
As a special case, the field at the centre of the loop is
obtained from the above equation by letting ๐‘ง = 0 :
๐ต0 =
๐œ‡0๐ผ
2๐‘…
For a coil of N turns,
๐ต =
๐œ‡0๐‘๐ผ
2๐‘…
The magnetic field lines from a circular loop are depicted
in Fig. 10.20. The direction of the field is as per the right
hand thumb rule: Curl the palm of your right hand along
the circular wire with the fingers in the direction of the
current. The stretched right hand thumb then gives the
direction of the magnetic field (Fig. 10.21). Thus, the
upper part of the loop seen in Fig. 10.20 may be regarded
as the North pole and the lower part as the South pole of a
bar magnet.
The magnetic moment ๐‘š of a circular loop is defined
as ๐‘š = ๐ผ๐ด, where ๐ด is a vector of magnitude ๐ด and
direction perpendicular to ๐ด. Using Eq. (10.56),
โˆด ๐ต๐‘ง =
๐œ‡0
2๐œ‹
๐‘š
๐‘ง3
๐ต๐‘ง =
๐œ‡0
4๐œ‹
2๐‘š
๐‘ง3
Note that ๐ต๐‘ง and ๐‘š are in the same direction,
perpendicular to the plane of the loop.
Using electrostatic analogue,
๐ธ =
2๐‘
4๐œ‹๐œ€0๐‘ง3
,
which is the electric field at an axial point of an
electric dipole.
Ampereโ€™s law
MCQS ON APPLICATIONS
OF AMPERE LAW - 1
MCQS ON APPLICATIONS
OF AMPERE LAW - 2
Q. Five very long insulated straight wire are bound together to form a small
cable. Current carried by the wires are I1 = 20A, I2 = -5A, I3 = 10A, I4 = 7A
and I5 = -12A. What is the magnetic induction at a perpendicular distance of 5
cm from the cable?
a) 60ยตT b) 70ยตT
c) 75ยตT d) 80ยตT
RADIUS AND TIME PERIOD
OF POSITIVE ION
It is clear that positive ions
arrive each time at the gap
between the dee exactly at
the instant alternating
potential can accelerate it
further
Application of
Ampereโ€™s law
2. solenoid
Inside the solenoid
the magic field is
uniform and magnetic
field lines are parallel
to the solenoid axis.
As ๐›‰ = ๐ŸŽ๐ŸŽ
๐‚๐จ๐ฌ ๐ŸŽ๐ŸŽ = 1
Application of
Ampereโ€™s law
3. Toroid
direction.
Force acting on a current carrying conductor in
Uniform Magnetic Filed
X X X X
X X X X
X X X X
X X X X

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