Unit 7: Sources of magnetic field Oersteds experiment. Biot and - PowerPoint PPT Presentation

Unit 7: Sources of magnetic field  Oersted’s experiment.  Biot and Savart’s law. Jean-Baptiste Biot Félix Savart  Magnetic field lined  Magnetic field created by a circular loop  Ampère’s law (A.L.). Applications  Straight current-carrying wire  Coil André Marie Ampère

Oersted’s experiment. 1820  1. If switch is off, there isn’t current and compass needle is aligned along north-south axis  2. If switch is on, current aligns compass needle F perpendicular to current.  3. If current flows in opposite direction, compass needle is aligned in opposite direction. F An electric current creates a magnetic field Tipler, chapter 27,2

Biot and Savart’s law i  Magnetic field created by a   current is perpendicular to d B current, and depends on the d l  intensity of current and distance P r from current.  Magnetic field created by a current element (Idl ) at a point P is:             i d l r i d l u r   0 0 r u d B r   r 3 2 4 r 4 r dl direction is the same as i  0 (vacuum magnetic permittivity)=4  10 -7 Tm/A Tipler, chapter 27-2

Biot and Savart’s law  Magnetic field created by a finite piece of wire is the sum (integral) of each current element at P: B i       B i d l r   0 d l P B   3 4 r r  A B A This equation can be applied to different conductor shapes, straight conductors, circular conductors,…….

Magnetic field lines  Magnetic field lines created by a straight current- carrying wire are circular in shape around conductor:   B B  B i Direction of magnetic field comes from right-hand or screw rule Tipler, chapter 27.2

Magnetic field lines   Magnetic field lines created B by a circular loop:  B i  B https://www.youtube.com/watch?v=V-M07N4a6-Y

Magnetic field lines  As magnetic poles cannot exist isolated (north pole or south pole), any field line exiting from a north pole must go to a south pole, and all magnetic field lines are closed lines.

Ampère’s law.  Ampère’s law relates the integral of magnetic field along a closed line and the intensity passing through a surface enclosed by this line. Closed line C must be chosen by us (if possible, should be a magnetic field line): I 1 I 2 ... I i        B d l I c 0 i i c Ampère’s law Tipler, chapter 27.4

Ampère’s law.  Each intensity has it own sign, according to the r¡ght-hand or screw rule. I 2 >0 I 1 >0 ... I>0 I i <0 c  Ampère’s law is equivalent (in Electromagnetism), to Gauss’s law in Electrostatics.

Ampère’s law.  It’s used to compute magnetic fields where symmetry exists.  In order to easily compute the integral of line, the chosen closed line C should have two features:  a) Modulus of magnetic field should be equal at every points on closed line C.  b) Magnetic field vector (B) should be parallel to closed line C at every points along C.    In this way:        B d l Bdl B dl BL c c c

Application of A.L: straight current-carrying wire.  Let’s take a straight current-carrying wire. Field lines of this conductor are circumferences. Choosing one of such lines of radius R, surface enclosed by such line and applying A.L:            B d l B dl B 2 R I 0 B L L L B R  I B  0 B B  2 R i Tipler, chapter 27.4

Force between two straight current-carrying wires  A conductor creates a magnetic field on second conductor and a force appears on this conductor. The same happens on first conductor.  B 1 I 2  d  F 21 F 12    I 1 B 2 http://www.youtube.com/watch?v=43AeuDvWc0k Tipler, chapter 27.4

Application of A.L: toroid (circular solenoid).  Applying A.L. to middle line of toroid and to circle enclosed by this line:            B d l B dl B 2 R NI 0 L L N turns  B Ni  0 B i R  2 R B i By applying A.L. at points outside of toroid, result is that magnetic  B=0 field is zero at any point outside B toroid. B  B=0 Tipler, chapter 27.4

Application of A.L: solenoid.  If L>>>r, the magnetic field inside a solenoid can be taken as uniform, and null outside the solenoid. From toroid (L=2  R):  Ni  0   B ni 0 N turns L L N Number of turns n  B r by unit of lenght L B B     Ni S Magnetic moment of a solenoid:    Magnetic moment by unit of volume inside   Ni S B    M a solenoid is called magnetization:  V SL 0