MAGNETIC FIELD
BIOT – SAVART’S LAW
The Biot – Savart law gives the
Relationship of magnetic field
at any point with current
Carrying element.
µo id sinθ
r2
4π
dB =
θ
idl
Current
element
In vector form :
µ i dl × r
B= 0 ∫
3
4π
r
r
FLEMING'S LEFT-HAND RULE
X
current
RIGHT-HAND RULE
B
If we stretch our finger’s
like Image, then our thumb
gives direction Force, Index
finger gives direction of
Magnetic Field & Middle
Finger gives current.
Current
Holding a currant carrying
conductor in right hand in
such a way that thumb Points
in the direction of current
and curling finger’s gives
direction of magnetic field.
Voltage sensitivity : S V =
θ
i2
i4
MAGNETIC FIELD OF LONG
SOLENOID :
r = average radius
N = Total number of
turns in toroid.
N
Winding
S
rr
i
MAGNETIC FIELD OF SOME SPECIAL
CURRENT CARRYING CONDUCTORS
Y
φ2
φ1
r
i
B=
P
µ oi
(Sinφ1 + Sinφ2 ) n
4 πr
Special case
For infinitely
long conductor.
B=
X
i
µi
θ
B= o (
o )n
2r 360
θ
r
r
B=
B
O
µ oi
n
2r
µ0 i n
2πr
µ0 i n
4r
r = radius of Coil.
i
B=
r
P
x
B
FLorentz = qE + q ( V x B )
i
anand_mani16
Anti-clockwise
→
v
θ
F = q(V × B) ,
F = q VB Sinθ
θ = Angle between direction of
motion of charge and magnetic Field.
. Power delivered by Magnetic Force
to Charged Particle is always zero.
X = distance
from the center
of coil.
B
Case 1:
When charged
particle is moving
v
parallel or
antiparallel to
magnetic Field:
Magnetic Force F = qvB sinθ = 0
x
x x
x v
x
x
F
B
x x
v x x
v
F
F
τ = NBiA Sinθ
N = Number of turns
A = Area , I = current
Magnetic moment −
M = iA
∴τ = M × B
Radius of circular- Path r =
2πm
qB
P
S
mV
qB
B
n
2π
v
r
ACW
+Ze
+
Fe
ω is angular velocity of
e–
I(current)
electron.
Magnetic Induction at Nucleus Position
B=
µoI µo ew
=
2r
4 πr
r = orbital Radius, I = orbital current
Magnetic Moment circular orbit
M = IA =
ewr 2 evr
, A = Area of orbit.
=
2
2
Work done in Rotating a coil
placed in magnetic Field:
Potential Energy of a Coil
Placed in Magnetic Field:
W = MB ( 1 - Cosθ )
U = - MB Cosθ
= − M.B
Here, M = Magnetic Moment
of coil.
Q
R
y
v
Case 3:
v
When charge
Particle is moving
in any orbitary
q
z
direction with
respect to Magnetic
pitch
Field:- Magnetic Force Helical motion radius
F = q (V × B) = qvB sin θ
Charge particle follow Helical path.
Radius of Helix – r = mV Sin θ = mV⊥
⊥
+
Charge Particle move un – deviated
Radius of Path is r =
I=
Torque Acting on current Carrying
Coil:
x x
x x
x
F
F
x x
v
x x
x x
+q
x x v
x x
o
x x x x x x
x
mv 2
mV
∴
= q vB ⇒ r =
r
qB
Time period – T =
Path of charged particle in External
Magnetic Field:-
DR. Anand Mani
Case 2:
When charge
Particle moving
Perpendicular
to magnetic Field:Magnetic Force –
F = qvB Sin900 = qvB
The orbital Current generated
by electron revolving around
eω
nucleus −
where,
M = Magnetic Moment
L = mvr – Angular Momentum
m = mass of particle.
h = Planck & Constant
→
B
Orbital Current
qL
M
q
=
M=
=
L 2m
2m
e = electronic charge
m = mass of electron
Magnetic →
moment M
Direction of current in Coil show’s
Polarity
Relation Between Magnetic Moment
and Angular Momentum of Charge
Particle
It is represented as:eh
µB =
= 0.923 × 10 −23 Am2
4 πm
→
F (Force vector)
8
O
µoir 2
2(x 2 + r 2 )3/ 2
The magnetic moment associated
with an electron which is revolving
in First orbit of an atom.
P = F . V = υ [∴ (F ⊥ V)
For Semicircular
arc.
B=
0
When a charge particle of charge q
moves with velocity in presence of
electric field E and Magnetic Field B
v
Formula
Bohr Magneton
q
charge
v
Shape of current
carrying conductor
Lorentz force
MAGNETIC FORCE ON A
MOVING CHARGED PARTICLE
B = µ0ni
n = Number of turn's per
unit length.
i = Current flowing
Core
φ Si nBA
=
=
V R
KR
When an electron revolves in a
bounded orbit around nucleus,
due to its movement it behaves
as a current carrying loop and
Produce magnetic Field. This is
Known as Atomic Magnetism.
i5
i3
i1
enclosed
; Here, n = N
2πr
Current
ATOMIC MAGNETISM
MOVING CHARGES AND MAGNETISM
B
MAGNETIC FIELD OF TOROID :
B = µ0ni
F
F = nBil
Clockwise
This Law states that the line
integral of magnetic field B
around a closed loop is equal to
µ0 times the net current enclosed
by the loop. φ B . dl = µ
i
∑
S
φ nBA
=
i
K
Current sensitivity : Si =
AMPERE’S CIRCUITAL LAW
o
re
Co
. In Equillibrium = τ = nBiA = Kφ
i =K φ
nBA
l
The Current Carrying Coil behaves
as a bar magnet and magnetic
moment of Such Coil Can be
expressed as M = niA ,
n = Number of Coils
A = Area
F
. Restoring Torque = τ = Kφ
φ = Deflection
. Denote going into the paper. x
Force
µ0 = 4π x 10 T.m/A
. Torque - τ = nBiA
n = Number of coils
A = Area
P dB
i
-7
It works on the principle that a current carrying Coil
in uniform magnetic Field, experience a Torque.
The Region around a magnet in
which its magnetic influence can
be experienced is called magnetic
Field. (B )
. S.I unit Tesla ( T ).
. Denote Coming out.
Y
CURRENT CARRYING LOOP
AS MAGNETIC DIPOLE
MOVING COIL GALVANOMETER
2 πr
Time Period – T =
qB
qB
https://www.anandmani.com/
qB
Force between two Parallel
Current Carrying Conductor’ s
µ ii
F1 = F2 = F = o 1 2 × L
2 πa
a = distance between two
wires.
L = Length of wires.
MAGNETIC EFFECT OF CURRENT
χ
Force on current carrying
conductor in magnetic field
In uniform Magnetic Field the
total force acting on conductor
of Length L is expressed as,
θ = Angle made by current
direction with magnetic Field.
i1
dF
F = i(L × B) = iLB Sin θ
i
https://discord.io/anandmani
i2
→
B
dl
a
t.me/anandmani001