Ampere's circuital law and its applications

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

1. Ampere’s Circuital Law and its Applications Presented by: Abdul Haseeb (18EL75 ) Ghulam Murtaza (18EL83) Tariq Ahmed (18EL68) Presented to: Mam Rabail Memon

2. Let’s consider a bar of magnetic material (iron) ,which is placed in a uniform magnetic field of strength H. Magnetic Permeability: Permeability of a magnetic material means its conductivity for magnetic flux.

3. we see the the magnetic flux density B develops in the iron bar.

4. Thus the iron bar becomes magnetize and develops its own magnetic field in the presence of external magnetic field,is magnetic permeability.

5. Magnetic permiability ; is the constant of proportionality between magnetic induction and magnetic field intensity.

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 Ampere’s Circuital Law

7. 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 Statement: B Figure 1: Ampere's law applied current carrying wire

8. 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

9. Applications of Ampere’s Circuital Law

10. Ampere’s Law has variety of Applications like mentioned below. Applications of Ampere’s Circuital Law

11. 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 APPLICATIONS OF AMPERE’S CIRCUITAL LAW A. Magnetic field (B) due to Current carrying wire Figure 1: Ampere's law applied to current carrying wire

12. 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

13. . According to Ampere's law B( = =   14 Since this path encloses the whole current then B     direction of B and dl is the same. Therefore angle between B and dl is 0 .  

14. Consider a current carrying cylinder as shown in figure 2(a). 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 B . Magnetic field (B)due to current carrying cylinder : Case 1: when r   Figure 2(a). current carrying conductor P

15. As Magnetic field and Length of conductor are parallel Cos 0=1 Circumference of Circle is  

16. 17 Case 2: when r   Consider a current carrying conductor as shown in figure 2 (b). 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

17. According to Ampere’s law B( = =   B     18       direction of B and dl is the same. Therefore angle between B and dl is 0 .    

18. 19 Case 3 : when   Consider a current carrying conductor as shown in figure 2 (c). 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

19. 20 As =H