Download Key Concepts Biot- Savart Law

Key
Concepts
A moving charge produces both electric field and magnetic field and both
magnetic field can exert force on it.
Note: In 1831, Michael Faraday discovered electromagnetic induction when he
found that a changing magnetic field generates an encircling electric field.
Magnetic induction produced by a current
BiotSavart
Law
Biot-Savart Law
• The magnitude of dB is proportional to sine, where 0 is the angle between the
vectors ds and
• The observations are summarized in the mathematical equation called the
Biot-Savart law (magnetic field due to the current-carrying conductor)
Magnetic Field Generated by Current in Straight Wire
Consider a field point P that is a distance R. from the axi
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Graph showing variation of B with respect to r
Magnetic
field due
to
straight
wire
A Long Straight Conductor
The thin, straight wire is carrying a constant current
Due to
long st.
Conducto
r
• If the conductor is an infinitely long, straight wire
1
= π/2 and
2
= - π/2
So equation becomes :
Solenoid
A solenoid is a coil of wire carrying an electric current.
The magnetic field is similar shape to that around a bar magnet.
The strength of the field increases with
1. the electric current
2. the number of turns in the coil
Solenoid
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For a solenoid of length L with current i:
B = u0 NI/L
Toroid
 The toroid has N turns of wire
 Field at appoint at distance r from center of toroid (loop1)
Toroid
There is no field outside the coil(loop2)
Current
carrying
sheet
Magnetic Induction due to current carrying Sheet
B=½
0I
Where I = Linear current density(A/m)
Thick
Sheet
Magnetic Induction due to Thick Sheet
Bout = ½
Bin = ½
0Id
0Jx
Current density JA/m2
Earth’s
magnetic
field
Gilbert’s Magnetism (Earth magnetic Field)
 The line of earth’s magnetic induction lies in a vertical plane
coinciding with the magnetic North – South direction at that
place .
 Earth’s magnetic axis is slightly inclined to the geometric axis of
earth and this angle varies from 10.5* to 20*(in degree)
 The earth magnetic poles are opposite to the geometric poles.
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 At a given place on the surface of earth , the magnetic meridian
and the geographic meridian may not coincide. The angle
between them is called “ Declination at that place”.
Let B = total magnetic induction of the earth at that point
Bv = the vertical component of B in meridian plane = B
BH = the horizontal component of B in meridian plane = B
Therefore
Ampere’s
Law
Lorentz
Force
=
Amperes Law
Earth’s magnetic Field
The magnetic field in space around an electric current is
proportional to the electric current which serves as its source.
Equation:
Lorentz Force
Lorentz force is the combination of electric and magnetic
force on a point charge due to electromagnetic fields. If a
particle of charge q moves with velocity v in the presence of an
electric field E and a magnetic field B, then it will experience a
force.
Motion of A charge in uniform magnetic field
 When v is || to B : motion will be in a st.line and F = 0
 When v is perpendicular to B: Motion will be in circular
path with radius R=mv/qB and angular velocity
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=
qB/m and F = qvB
 When v is at angle
to B : motion will be helical
with radius with R = mvsin /qB
Pitch 2 mvcos /qB and F = qvBsin
Magnetic force on a st. current carrying wire
L = length of conductor in direction of current in it.
B = magnetic induction.
In general:
F=∫
S
Magnetic interaction force between two parallel long straight currents
 Repulsion , if current are anti- parallels
 Attraction , if current are parallels
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Magnetic Torque on a closed current circuit
Note: this expression can be used only if B is uniform otherwise
calculus will be used.
Moving
Moving coil Galvanometer
coil
Deflecting torque (Td) = restoring torque(Tr)
Galvano
meter
Force on random shaped conductor in magnetic field:
 Magnetic force on a loop in a uniform B is zero
 Force experienced by a wire of any shape is equivalent to force
on a wire’s end point.
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Magnetic moment of a rotating charge
If a chare is rotating at angular velocity w,
It equivalent current is given as I =
, and its magnetic
moment is M = 1/2q R2.
Extra :
Note:
The rate of magnetic moment to angular momentum
of a uniform rotating object which is charged
uniformly is always a constant . irrespective of the
shape of conductor
M/L = q/2m
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