Hukum Ampere

Ampere’s Law

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

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

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

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

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

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

Quiz c Currents of 1A, 5A, 2A, flowing in 3 wires as shown a b 1A What is B.ds through loops a, b, c, d? 5A 2A B.ds -1m0 +3m0 +4m0 +6m0 a b c d

Examples of using Ampere’s Law

Examples Long-straight wire Insider a long straight wire Toroidal coil Solenoid

Long Wire

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

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

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.

Di dalam suatu kawat

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 r A

Medan B dari suatu kawat panjang

Toroidal Coil

Toroidal Coil I0 r 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

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

Toroidal Coil I0 r 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

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

Solenoid

Infinitely Long Solenoid Wire carrying a current of I0 wrapped around with n coils per unit length Zoom looks very similar to the toroid with a very large radius

Infinitely Long Solenoid Wire carrying a current of I0 wrapped around with n coils per unit length Field at centre is same as torus of infinite radius

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

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