2. What is Biot Savart’s
Law?
• The Biot Savart Law is an equation
describing the magnetic field generated
by a constant electric current.
• It relates the magnetic field to the
magnitude, direction, length, and
proximity of the electric current. Biot–
Savart law is consistent with both
Ampere’s circuital law and Gauss’s
theorem.
• The Biot Savart law is fundamental to
magnetostatics, playing a role similar to
that of Coulomb’s law in electrostatics.
3. Biot Savart Law Statement:
• This is Biot Savart law statement:
• Where, k is a constant, depending upon the magnetic properties of the medium and system of
the units employed. In SI system of unit.
4. • Therefore, final Biot Savart law derivation is,
Where
•μ0 is the permeability of free space and is equal to 4π × 10-7 TmA-1.
The direction of the magnetic field is always in a plane perpendicular to the line of element and
position vector. It is given by the right-hand thumb rule where the thumb points to the direction of
conventional current and the other fingers show the magnetic field’s direction.
5. • A conductor which carries current (I) with the
length (dl), is a basic magnetic field source.
The power on one more related conductor can
be expressed easily in terms of the magnetic
field (dB) due to the primary.
• The magnetic field dB dependence on the ‘I’
current, dimension as well as direction of the
length dl & on distance ‘r’ was primarily
estimated by Biot & Savart.
6. General
Methodology
to Follow:
Source point:
• Choose an appropriate coordinate system and
write down an expression for the differential
current element Ids , and the vector r’
describing the position of Ids.
• The magnitude r’= r’ is the distance between I
dš and the origin. Variables with a "prime" are
used for the source point.
7. Field point:
• The field point P is the point in space where
the magnetic field due to the current
distribution is to be calculated.
• Using the same coordinate system, write down
the position vector rp, for the field point P.
• The quantity rp = rp is the distance between
the origin and P.
8. Relative
position
vector
• The relative position between the source point
and the field point is characterized by the
relative position vector r=rp-r'. The
corresponding unit vector is
• Where r=r = rp-r’ is the distance between the
source and the field point P.
9. Relative
Position
Vector:
• Calculate the cross-product ds x r or ds x r. The
resultant vector gives the direction of the
magnetic field B, according to the Biot -Savart
law.
• Substitute the expressions obtained to dB and
simply as much as possibly.
• Complete the integration to obtain B if
possible. The size or the geometry of the
system is reflected in the integration limits.
• Change of variables sometimes may help to
complete the integration.
10. Important
Examples
Magnetic Field Due to a Finite Straight
Wire:
• A Thin, straight wire carrying a current I is
placed along the x-axis. Evaluate the
magnetic field at point P.
• Note that we have assumed that the leads
to the ends of the wire make canceling
contributions to the net magnetic field at
the point P.
Magnetic Field Due to a Circular Current
Loop:
• A circular loop of radius R in the ry plane
carries a steady current I
11.
12.
13.
14. Applications
MAGNETIC FIELD DUE TO STEADY
CURRENT IN AN INFINITELY LONG
STRAIGHT WIRE.
FORCE BETWEEN TWO LONG AND
PARALLEL CURRENT CARRYING
CONDUCTOR.
MAGNETIC FIELD ALONG AXIS OF A
CIRCULAR CURRENT CARRYING
COIL.
15. Applications
This law can be used for calculating
magnetic reactions even on the level of
molecular or atomic.
It can be used in the theory of
aerodynamic for determining the
velocity encouraged with vortex lines.
Magnetic Field at the center of a
current carrying arc.
