2. Introduction
Biot-Savart
Law (Magnetic Field due to a Current)
Magnetic Field due to a Straight (infinitely) l
Magnetic Field due to a circular current loop
Current Loop and Magnetic Dipole

3. The term "magnetic effects of current "
means that " a current flowing in a wire
produces a magnetic field round it ". the
magnetic effect of current was discovered
by Oersted found that a wire carrying a current
was able to deflect a magnetic needle.

4. Forces acting on charges moving in magnetic and
electric fields are used to deflect and focus beams of
electrons in many practical devices. Perhaps the most
common (but rather complicated) example of this is the
TV tube. The image on the face of the tube is due to a
beam of electrons hitting a coating of a material called
phosphor which emits light on being struck. The beam
of electrons is deflected in a very complex way be
electric fields applied to parallel plates between which
the beam passes.

5. The medium around a charge is
always under stress and that a force
acts on a positive or negative charge
when placed in that medium this
reason in which stress exists is called
an electric field. It is also known as
a dielectric field or electrostatic field.

7. A static charge produce a radial electric field that
aligns grass seeds to show the field direction. We
usually represent the field with the thin solid lines
(with arrows) that we call lines of force.
Electrostatics is that branch of science which deals
with the phenomena associated with electricity at rest.
As we know that generally an atom is electrically
neutral i.e. in a normal atom the aggregate of positive
charge on protons is exactly equal to the aggregate of
negative charge on electrons.

9. A magnetic compass needle, brought close to a straight wire
carrying an electric current, aligned itself perpendicular to the
wire . More precisely , the alignment is tangential to a circle
which has the wire as centre , and which has its plane
perpendicular to the wire. Oersted also notice that reversing
the direction of current nearly reversed the direction in which
the needle pointed i.e. needle pointing N-S turned to S-N. from
such observation he conclude that a magnetic field is
associated with an electric current and that it is this magnetic
field which tends to align a magnetic needle much as the
earth's magnetic field dose.

10. The elementary source of magnetic force is a small length dl (or a length
element) of a conductor carrying a current I. The force on another
similar conductor can be expressed conveniently in terms of a magnetic
field dB due to the first. The dependence of such magnetic field on the
current I, on the size and orientation of the line element d1, and on the
distance r from it was guessed at by Biotand Savart from measure
ments on finite (not infinitesimal) current-carrying wires with simple
shapes, e.g. lines, rectangles and circles. These measurements were of
forces as well as comes equilibrium near such wires. This direction turns
out to be that of the total resultant magnetic field, i.e., the vector sum
of the magnetic fields due to the current-carrying wire and the earth.

11. The magnitude of the magnetic field dB at a distance r from a
current element dl carrying a current I is found to be
proportional to I, to the length dl and inversely to the square
of the distance |r|. The direction of the magnetic field is
perpendicular to the line element dl as well as the radius r.
µ o I dl x r
dB = ------- --------- tesla (Wb/m 2 )
4 p r 3

12. The medium around a charge
is always under stress and
that a force acts on a positive
or negative charge when
placed in that medium this
reason in which stress exists
is called an electric field. It
is also known as a dielectric

14. A static charge produce a
radial electric field that
aligns grass seeds to show
the field direction. We
usually represent the field
with the thin solid lines
(with arrows) that we call

15.
Let us assume we have a uniform
electric field E (constant
direction and magnitude) in some
region of space, and a dipole
moment vector makes an
angle q with the field E. The
positive charge feels a force qE,
So the net force on a dipole in a

17. Even though the two forces on the ends of the dipole cancel as
free vectors, they act at different points. This means that they
give rise to a torque on dipole. The turning effect of this torque
is to reduce the angle q towards zero, and make the dipole
moment vector become parallel to the field.
The magnitude of the torque with respect to the centre of
the dipole is the sum of the two forces times their lever arms:
|t| = 2q |E|a sin q = |p||E| sin q
t = p * E newton-meter
Thus in a uniform electric field, a dipole align itself parallel
to the field, when the orientation is some non zero
angle q there must be potential energy stored in the dipole
from the preferred orientation q = 0 to some nonzero q, you
have to oppose the torque due to the field and do some work.

18. Both magnetic and electric fields depend inversely on the square of
the distance between the source and the field point.
The electric field is produced by a scalar source, i.e., the
electric charge, which is specified completely by a number, positive or
negative, in some unit. The magnetic field is produced by a vector
source, i.e., by a current element which has a magnitude I|dl| and a
direction along the line element dl.
The electric field is along the radius vector joining the source and
field point, while the magnetic field is perpendicular to the radius
vector (and to the current element vector).
Both electric and magnetic fields are proportional to the source
strength, namely charge q and current element I dl, respectively.

19. It is proportional to the current I.
It is inversely proportional to the
distance R.
Its size is rather small.
The magnetic field is in a direction
perpendicular to both the straight wire and
the vector AP.

20. Consider a straight infinitely long wire carrying a steady
current I. The line AP is perpendicular to the wire, and is of
length R. From the Biot-Savart law, the magnetic field dB
due to a small element dl of the wire near the point O at a
distance |r| = r from P (OP=r) is
µo I
dl x r
dB = -------
---------

21. Since the current element dl and the vector r make an angle q with each other, the
product dl*r has a magnitude dlr sin q. It is directed perpendicular to both dl and
r. This is the direction perpendicular to the plane of the paper and going into it, as
is clear from the right handed corkscrew rule (link) (direction of advance of a right
handed corkscrew turning from dl to r).
µo I dl sin q
dB = ---- -------k
4 p r2
The magnetic field at a point P due to a infinite (very long) straight wire
carrying a current I is proportional to I, and is inversely proportional to the
perpendicular distance R of the point from the wire. The integral J has a value of
2, so that
µo Ι
B
= −−−− −−−− k tesla (Wb/m2)
2 π R

23. circle, centered at A has the magnitude
µo Idl µo Idl
dB = ----- ------- = ---- ---------
4 p |AP|2 4 p (R2 +
a2)
This field can be resolved into two
components one along the axis OP, and the
other (PS) perpendicular to it. The latter
component is exactly cancelled by the
perpendicular component (PS’) of the field
due to a current and centred at A’. Field

24. µo I dl
dB (along OP) = ---- ---- { sin ø }
4 p r2
µo I dl a
= --- --------------
4 p R2 + a2 (R2 + a2)1/2
µo I a
= --- ------- dl
4 p (R2 + a2)3/2
The magnetic field due to the circular current
loop of radius a at a point which is a
distance R away, and is on its axis (i.e. on a
line perpendicular to the plane of the circle
and passing through its center) is

25. Ι 2
a
B
= −−− −−−−−−− i
(i is the unit vector
along OP, the x-
axis) tesla
(Wb/m ) 2
2

26. At distances R large compared to a we canapproximate
(R2+a2) 3/2 by R3 and the field B then has the magnitude
m o (2I) (pa 2 )
B = --- -------
4p (R 3 )
mo 2 I A
B = --- ----- Where A is the area of the circular current loop.
3

27. At the other extreme of distance, namely R = 0, i.e. at the
center of the loop the magnitude of the field is
mo Ι
∴ B
= -----
2a
which depends on the loop radius a in the same way as the
magnetic field of a straight long wire depends on the distance
R from it.

28. Magnetic dipole moment M with the
circular current loop carrying a
current I and of area A. The
magnitude of m is
|m|
=IA
or
m = I A
Further, the direction of the
magnetic dipole moment is