This document discusses Biot-Savart's law, which describes the magnetic field generated by a current-carrying conductor. It states that the magnetic field dB at a point P due to a current element dl is directly proportional to the current I and dl, and inversely proportional to the square of the distance r between them. It also depends on the sine of the angle θ between dl and r. The document presents Biot-Savart's law in both scalar and vector forms, and compares it to Coulomb's law for electric fields. It also discusses relative permeability and the similarities and differences between Biot-Savart's and Coulomb's laws.

1. Priyanka Jakhar
Physics Lecturer
GGIC Vijay Nagar
Ghaziabad U.P.
Class 12th Physics
Biot – Savart’s Law

2. Biot – Savart’s Law:
Biot-Savart law was created by two French physicists, Jean Baptiste Biot and Felix Savart derived the
mathematical expression for magnetic flux density at a point due to a nearby current-carrying conductor,
in 1820.
Biot-Savart law gives this relation between current and magnetic field.
Biot-Savart’s law is an equation that gives the magnetic field produced due to a current
carrying segment.
The Biot Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb’s law in
electrostatics.
The strength of magnetic fielddB due to a small current element dl carrying a current I at a point P
distant r from the element is directly proportional to I, dl, sin θ and inversely
proportional to the square of the distance (r2)
where θ is the angle between dl and r.
θ
x
P
dl r
i) dB α I
ii) dB α dl
iii) dB α sin θ
iv) dB α 1 / r2
dB α
I dl sin θ
r2
dB =
4π r2
P’
I
μ0I dl sin θ

3. If θ = 0° , The point P lies on the axis of the linear conductor carrying current
If θ = 90° The point P lies at the perpendicular position with respect to element which is maximum
If θ = 180° ,then dB = 0 ,which is minimum.
dB =
4π r2
μ0I dl sin θ dB =
4π r2
μ0I dl sin 90°
dB =
4π r2
μ0I dl sin 0°
dB =
4π r2
μ0I dl sin θ
dB =
If If the magnetic field is taken due to the entire length of a conductor
4π r2
μ0I dl sin 180°
μ0I dl sin θ
dB =
4π r2
dB = 0
dB =
4π r2
μ0I dl
dB =
4π r2
μ0I dl sin θ
dB = 0
B =
∫∫

4. Biot – Savart’s Law in vector form :
dB =
μ0 I dl x r
4π r2
dB =
μ0 I dl x r
4π r3
Value of μ0 = 4π x 10-7 TmA-1
or Wb m-1 A-1
Direction of dB is same as that of direction of dl x r which can be determined by Right Hand Screw Rule.
It is emerging at P’ and entering at P into the plane of the diagram.
Current element is a vector quantity whose magnitude is the vector product of current and length of
small element having the direction of the flow of current. ( I dl )
x
dB =
μ0 j dV sin θ
In vector formr2
4π
Biot – Savart’s Law in terms of current density :
μ0( j x r ) dV
dB =
4π
4π
μ0 q ( v x r )
r3
r3
Biot – Savart’s Law in terms of charge and its velocity :
dB =

5. Relative permeability :-- The ratio of permeability of the medium to permeability of free space
is known as Relative permeability .
It is represented by μr
μr is dimensionless quantity .
It has no unit .
μr
μ
μ0
=
Relation between permeability and permittivity :--
μ0 ε0 =
c2
1
Units and dimensions of permeability :--
The permeability measures the ability of the material to allow the magnetic lines of force to
pass through it.
The magnetic permeability is dimensionally represented as [M1 L1 T-2 A-2] .
The unit is N⋅A−2 for SI unit .
The symbol is μ for medium .
The magnetic permeability in a vacuum is expressed as μ0 .
μ0 = 4π × 10-7 weber per ampere-metre .

6. Basis For Comparison Permittivity Permeability
Definition The Permittivity measures the
resistance offer by the material in the
formation of an electric field.
The permeability measures the
ability of the material to allow
the magnetic lines of force to
pass through it.
Symbol ε μ
Formula Ratio of displacement field strength to
the electric field strength.
Ratio of magnetic field density
and magnetic field strength.
SI Unit Faraday/meter Henry/meter
Physical Basis Polarization Magnetization
Free Space The permittivity of the free space is
8.85 F/m.
The permeability of the free
space is 1.26 H/m.
Field Electric Field Magnetic Field
Used in Capacitor Inductor and Transformer core

7. Similarity Between Biot Savart’s Law And Coulomb’s Law
1. Field at any point vary inversely as the square of the distance .
2. Both obey superposition principle
3. Both sources Idl for magnetic field and q for electric field are linear in nature.
4. Magnetic field due to a moving charge (Biot-Savart law) is:
μo × idl(sinθ)
B =
4π r2
5. Electric field due to a point charge (Coulomb’s law) is :
1 × q
E =
4πƐo r2
Differences Between Biot Savart’s Law And Coulomb’s Law
1. Electric field is produced by a scalar source (q) where as Magnetic field is produce by
vector source (I dl)
2. Electric field is acting along the displacement vector where as Magnetic field acts
perpendicular to I x r.
3. Electric field is not depends of θ where as Magnetic field depends upon θ.