EMLAB 1 Chapter 9. Magnetic forces, materials, and inductance

EMLAB Force on a moving charge 1) Electric force 2) Magnetic force F E F B v (Lorentz force) (Coulomb force)

EMLAB 3Examples Electron beams are deflected by Lorentz force

EMLAB 4Examples CRT use Lorentz force to steer electrons emitted from the cathode.

EMLAB Force on a differential current element B B

EMLAB 6B

7 Example 9.1

EMLAB Force between differential current elements

EMLAB Force and Torque on a closed circuit F F B F F B B is slowly varying function over the integration path.

EMLAB 10 Simple motor Magnet

EMLAB The nature of magnetic materials - F F Electron : 1) orbital spin 2) electron spin F F B B

EMLAB 12 Diamagnetic : 반자성체  <1 Paramagnetic : 상자성체   1 Magnetic moments of an electron pair in valence band cancel each other. Magnetic moment of an unpaired electron is not canceled. Paramagnetic material is influenced by external magnetic field, tend to align its magnetic moment along the external field.

EMLAB 13 Diamagnetic : 반자성체  <1 Paramagnetic : 상자성체   1 Ferromagnetic : 강자성체  >> 1 Antiferromagnetic : Ferrimagnetic : Ferrite (small  ) H B B-H curve

EMLAB 14 Magnetization and demagnetization H not applied H applied

EMLAB 15 (a) Hard disk tracks. (b) Sketch of qualitative shapes of hysteresis curves required for the head and track magnetic materials. The magnetic head aerodynamically flies over the disk surface at a distance above it of only about 1mm while following the surface profile. In the figure, the surface profile is shown as ideally flat, which in practice is not the case. Hard disk application

EMLAB Magnetic boundary conditions 1) Normal component 2) Tangential component If either of the two medium is conductor, Jh is nonzero with h→0.

EMLAB Magnetic circuit Reluctance Resistance

EMLAB 18 If the permeability of a magnet is larger than the surrounding medium, very small leakages in magnetic flux can be observed. Static Current Flow and Magnetostatic Simulation of a simple C-magnet

EMLAB 19 Comparison of Magnetic and electric circuits

EMLAB 20 Example 9.9

EMLAB 21 1) Faraday experiment N S Electromotive force (emf) (-) sign explains the emf is induced across the terminals of the coil in such a way that hinders the change of the magnetic flux nearby. 1.A time-varying flux linking a stationary circuit. 2.A constant magnetic flux with a moving circuit 3.Combination of the above two cases Situations when EMF is generated Faraday’s law

EMLAB 22 +V-+V- (1) A time-varying flux linking a stationary circuit. Time varying

EMLAB 23 (2) A constant magnetic flux with a moving circuit (1) A phenomena observed by a stationary person Direction of induced current Due to the motion of a conducting bar, the charges in it moves in the (+y) direction. The moving charges experience Lorentz force such that 1.Effectively, the motion of bar generates electric field which has the strength of (v x B) 2.emf = Ed = vBd

EMLAB 24 F i : Inertial force An elevator which is accelerated in downward direction. Acceleration of a ball observed by a stationary rabbit. Acceleration of a ball observed by moving Pikachu. Analogy to inertial force

EMLAB 25 (3) Combination of the two

EMLAB 26 Example : AC generator A simple AC generator

EMLAB 27 Example : Hard disk head

EMLAB 28 Concept of inductance Current Magnetic flux :

EMLAB 29 Mutual Inductance (1) When the secondary circuit is open The current flowing through the primary circuit generates magnetic flux, which influences the secondary circuit. Due to the magnetic flux, a repulsive voltage is induced on the secondary circuit.

EMLAB Magnetic energy Self energy : The energy needed for the circuit to have a current I flow in spite of the repelling electromotive force from Faraday’s law. (Initially, this circuit has a zero current flowing. Then, the current increases to I.) (To support current i(t), the current source should provide additional voltage which cancels induced voltage by Faraday’s law.)

EMLAB 31 Work to move current loop I BABA If we want to move a current loop with I flowing in a region with a magnetic flux density B, energy should be supplied from an external source. The voltage induced in the current loop hinders the current flow, which should be canceled by an external source.

EMLAB 32 B The energy is equal to assemble circuits with current I i. Magnetic energy : Mutual interaction IiIi IjIj Energy needed to assemble I 1, I 2 ~I N in a free space. Energy needed to disintegrate I 1, I 2,~,I n. Magnetic material (Including self energy)

EMLAB 33 B The energy needed to assemble current loops with constant current sources I i. IiIi IjIj Energy needed to assemble Energy needed to disassemble W i,j 9.9 Magnetic energy

EMLAB 34 Magnetic energy by Field variables R If the integration surface extend to infinity, the second term banishes.

EMLAB 35 Inductance calculation by Energy I The induced voltage is generated by the circuit itself. - V +

EMLAB 36 Mutual Inductance Field equations are useful in deriving mutual inductances. circuit 1 circuit 2 The current flowing through the circuit 1 generates magnetic flux, which induces emf in the second coil.

EMLAB 37 Example 9.9

EMLAB 38

EMLAB For values of B below the knee on the magnetization curve for silicon steel, approximate the curve by a straight line with μ = 5 mH/m. The core shown in Fig has areas of 1.6 cm 2 and lengths of 10 cm in each outer leg, and an area of 2.5 cm 2 and a length of 3 cm in the central leg. A coil of 1200 turns carrying 12 mA is placed around the central leg. Find B in the: a) center leg (b) center leg, if a 0.3-mm air gap is present in the center leg:

EMLAB 40