Hukum Ampere

1. Hukum Ampere

2. Ampere’s Law

3. Medan magnetik dari kawat lurus panjang gunakan Hk Biot-Savart r I Ambil vektor pendek , ds B ds Perkalian skalar antara B & vektor pendek ds adalah:

4. Jumlah B.ds di sekitar lintasan lingkaran r I B Jumlahkan ini untuk seluruh cincin ds Keliling lingkaran

5. Jumlah B.ds di sekitar lintasan lingkaran N.B. this does not depend on r In fact it does not depend on path Ampere’s Law: on any closed loop where I is the current flowing through the loop

6. I B B I I I Hukum Ampere Sign comes from direction of loop, current & right hand rule

7. Sign comes from direction of loop, current & right hand rule I I I B B B I I I Hukum Ampere

8. Hukum Ampere • No Different Physics from Biot-Savart Law • Useful in cases where there is a high degree of symmetry • C.f. Coulomb’s Law and Gauss’s Law in electrostatics

9. a b c Quiz Currents of 1A, 5A, 2A, flowing in 3 wires as shown 1A What is B.ds through loops a, b, c, d? 5A 2A

10. Examples of using Ampere’s Law

11. Examples • Long-straight wire • Insider a long straight wire • Toroidal coil • Solenoid

12. Long Wire

13. Magnetic Field from a long wire By symmetry r Ampere’s Law on Loop 2 I B||(r1) Loop1 Br2 Br1 B||(r1)

14. Magnetic Field from a long wire r I For any closed Ampere Loop the radial components will always cancel out By symmetry Br3 Br4 Loop 2 Loop 3 Br2 Br1 Br1 Thus there is no way to balance a current by a radial component or produce a radial component from a current Br2

15. Magnetic Field from a long wire Tangential component Take a circle of radius r as the Ampere Loop r I Tangential component By symmetry at constant r L.H.S. or L.H.S. = R.H.S Q.E.D.

16. Di dalam suatu kawat

17. Di dalam suatu kawat berarus I0 Kita pilih loop Ampere berupa lingkaran dengan jari-jari r Asumsikan rapat arus adalah homogen sehingga arus yang mengalir dalam loop adalah Sama seperti sebelumnnya A r

18. B R r Medan B dari suatu kawat panjang

19. Toroidal Coil

20. r Toroidal Coil I0 Toroid has N loops of wire, carrying a current I0 Ampere Loop, circle radius r No current flowing through loop thus B = 0 inside the Toroid

21. r Toroidal Coil Ampere Loop, circle radius r I0 For each wire going in there is another wire comeing out Thus no nett current flowing through loop thus B = 0 outside the Toroid

22. r Toroidal Coil I0 Zoom Toroid has N loops of wire For each loop of the coil an extra I0 of current passes through the Ampere Loop Ampere Loop, circle radius r

23. ds r Medan B di dalam Toroida • Toroid berbentuk donut dengan dililiti koil. • Maka,

24. Solenoid

25. Infinitely Long Solenoid Wire carrying a current of I0wrapped around with n coils per unit length Zoom looks very similar to the toroid with a very large radius

26. Infinitely Long Solenoid Wire carrying a current of I0wrapped around with n coils per unit length Field at centre is same as torus of infinite radius

27. Medan magnet di dalam Solenoida • Jika solenoida terdiri dari jumlah lilitan N dan panjang adalah l, maka: l ds

28. Resume • Hukum Ampere • Lebih mudah dipakai dibandingkan Hukum Biot-Savart dalam banyak kasus • Contoh • Kawat panjang • Dalam kawat • Toroida • Solenoida