Ampere's circuital law and its applications Magnetic Field on a current carrying cylinder.

2. Let’s consider a bar of magnetic material (iron) ,which is placed
in a uniform magnetic field of strength H.

6. Introduction
 A useful law that relates the net magnetic field along a
closed loop to the electric current passing through the
loop.
• First discovered by André-Marie Ampère in 1826

8.  The integral of magnetic field density B
along a closed path is equal to the product of
current enclosed by the path and
permeability of the medium.
 Mathematically ,
8
B
Figure 1: Ampere's law applied
current carrying wire

9.  In other words Ampere’s circuital law is defined as
“The integral of magnetic field intensity (H) along a closed path is equal
to the current enclosed by the path”.
9

11.  Ampere’s Law has variety of
Applications like mentioned below.

12.  Consider a long current carrying wire is
along the z-axis as in Figure 1.
 Let I be the current flowing through the wire
in the direction as shown in figure 1.
 The magnetic field is produced around the
conductor .
12
Figure 1: Ampere's law applied to
current carrying wire

13.  The magnetic field lines of forces
are concentric circles in XY
plane.
 To determine H at an observation
point P, we allow a closed path
passes through P. This path, on
which Ampere's law is to be
applied, is known as an Amperian
path.
13

14.  . According to Ampere's law
𝑩𝒅𝒍 = 𝜇0 𝐼
B(2πρ) = 𝜇0I
𝐵/𝜇0=
𝐼
2𝜋𝜌
𝐻=
𝐼
2𝜋𝜌
14
Bdl𝑐𝑜𝑠𝜃 = 𝜇0 𝐼
B 𝑑𝑙 = 𝜇0 𝐼
Bdl𝑐𝑜𝑠0 = 𝜇0 𝐼
direction of B and dl is the same. Therefore angle
between B and dl is 0°.

15.  Consider a current carrying cylinder as
shown in figure 2(a).
 𝜌 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑑𝑖𝑢𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛.
 The magnetic field is present around a
conductor in the form of concentric circle.
 The point P is located outside the surface
and the distance from center to point P is
denoted by r.
15
Figure 2(a). current carrying conductor
P

16. • As Magnetic field and Length of conductor are parallel
Cos 0=1
Circumference of Circle is 𝐴 = 2𝜋𝑟

17. 17
 Consider a current carrying conductor as
shown in figure 2 (b).
 𝑟 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑑𝑖𝑢𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛 .
 The magnetic field is present around a
conductor in the form of concentric circle.
 The point P is located at the surface and the
distance from center to point P is denoted by
r. figure 2 (b).
P
P

18. • According to Ampere’s law
B(2πr) = 𝜇0I
𝐵/𝜇0=
𝐼
2𝜋𝑟
𝐻=
𝐼
2𝜋𝜌
B 𝑑𝑙 = 𝜇0 𝐼
Bdl = 𝜇0 𝐼
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𝑩𝒅𝒍 = 𝜇0 𝐼
Bdl𝑐𝑜𝑠𝜃 = 𝜇0 𝐼
Bdl𝑐𝑜𝑠0 = 𝜇0 𝐼
direction of B and dl is the same. Therefore angle
between B and dl is 0°.
𝜌 = 𝑟

19. 19
 Consider a current carrying conductor as
shown in figure 2 (c).
 𝜌 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑑𝑖𝑢𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛
 The magnetic field is present around a
conductor in the form of concentric circle.
 The point P is located inside the surface and
the distance from center to point P is denoted
by r.
figure 2(c)
P

20. 20
• As 𝐵/𝜇0=H