Slide 1Lightning Review19.7 Motion of Charged Particle in magnetic fieldSlide 4Example 1 : Proton moving in uniform magnetic fieldExample 2:19.8 Magnetic Field of a long straight wireMagnetic Field due to CurrentsSlide 9Slide 10Slide 1119.9 Magnetic Force between two parallel conductorsSlide 13Definition of the SI unit AmpereExample 1: Levitating a wireSlide 16Example 2: magnetic field between the wires19.10 Magnetic Field of a current loop19.11 Magnetic Field of a solenoidSolenoid MagnetSlide 21Example: Magnetic Field inside a Solenoid.Slide 231101/14/1901/14/19General Physics (PHY 2140)Lecture 14Lecture 14 Electricity and MagnetismMagnetism Ampere’s lawApplications of magnetic forces Chapter 19http://www.physics.wayne.edu/~apetrov/PHY2140/2201/14/1901/14/19Lightning ReviewLightning ReviewLast lecture: 1.1.MagnetismMagnetismGalvanometerGalvanometerTorque on a current loopTorque on a current loopReview Problem: A rectangular loop is placed in a uniform magnetic field with the plane of the loop perpendicular to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop:1. a net force.2. a net torque.3. a net force and a net torque.4. neither a net force nor a net torque.sinF qvB q=sinF BIl q=sinNBIAt q=3301/14/1901/14/1919.7 Motion of Charged Particle in magnetic field19.7 Motion of Charged Particle in magnetic fieldConsider positively charge Consider positively charge particle moving in a uniform particle moving in a uniform magnetic field.magnetic field.Suppose the initial velocity of the Suppose the initial velocity of the particle is particle is perpendicular to the perpendicular to the direction of the fielddirection of the field..Then a Then a magnetic forcemagnetic force will be will be exerted on the particle… exerted on the particle…  FvqrBinWhere is it directed?Where is it directed?… … and make it follow a and make it follow a circular circular pathpath..Remember that v F^r ur4401/14/1901/14/19The magnetic force produces a centripetal acceleration.The particle travels on a circular trajectory with a radius:cF ma=ur r2cvar=22mvF qvB= =mvrqB=sin sin 90 1q = =o5501/14/1901/14/19Example 1 : Proton moving in uniform magnetic fieldExample 1 : Proton moving in uniform magnetic fieldA proton is moving in a circular orbit of radius 14 cm in a uniform A proton is moving in a circular orbit of radius 14 cm in a uniform magnetic field of magnitude 0.35 T, directed perpendicular to the magnetic field of magnitude 0.35 T, directed perpendicular to the velocity of the proton. Find the orbital speed of the proton.velocity of the proton. Find the orbital speed of the proton.Given:r = 0.14 mB = 0.35 Tm = 1.67x10-27 kgq = 1.6 x 10-19 CmvrqB=qBrvm=Find:v = ?Recall that the proton’s radius would be( )( )( )( )19 22761.6 10 0.35 14 101.67 104.7 10msC T mkg- --� �=�= �Thus6601/14/1901/14/19Example 2: Example 2: Consider the mass spectrometer. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m=2.18×10-26 kg.7701/14/1901/14/1919.8 Magnetic Field of a long straight wire19.8 Magnetic Field of a long straight wireDanish scientist Hans Oersted (1777-1851) discovered Danish scientist Hans Oersted (1777-1851) discovered (somewhat by accident) that an electric current in a wire (somewhat by accident) that an electric current in a wire deflects a nearby compass needle.deflects a nearby compass needle.In 1820, he performed a simple experiment with many In 1820, he performed a simple experiment with many compasses that clearly showed the presence of a compasses that clearly showed the presence of a magnetic field around a wire carrying a current.magnetic field around a wire carrying a current.I=0I8801/14/1901/14/19Magnetic Field due to CurrentsMagnetic Field due to CurrentsThe passage of a steady current in a wire produces a The passage of a steady current in a wire produces a magnetic field around the wire.magnetic field around the wire.Field form concentric lines around the wireField form concentric lines around the wireDirection of the field given by the right hand rule.Direction of the field given by the right hand rule.If the wire is grasped in the right hand with the thumb in the If the wire is grasped in the right hand with the thumb in the direction of the current, the fingers will curl in the direction of direction of the current, the fingers will curl in the direction of the field (the field (second right-hand rulesecond right-hand rule).).Magnitude of the field Magnitude of the field I2oIBrmp=9901/14/1901/14/19Magnitude of the fieldIrBo called the permeability of free space2oIBrmp=704 10 T m Am p-= � �101001/14/1901/14/19Andre-Marie AmpereAmpere’s LawConsider a circular path surrounding a current, divided in segments l, Ampere showed that the sum of the products of the field by the length of the segment is equal to o times the current.IrBloB l ImD =�P111101/14/1901/14/192oB l B l B r Ip mD = D = =� �P P PConsider a case where B is constant and uniform:Then one finds:2oIBrmp=P121201/14/1901/14/1919.9 Magnetic Force between two parallel conductors19.9 Magnetic Force between two parallel conductors131301/14/1901/14/19222oIBdmp=ld12F1B2I1I22 1 21 2 1 12 2o oI I I lF B I l I ld dm mp p� �= = =� �� �1 212oI IFl dmp=Force per unit length141401/14/1901/14/19Definition of the SI unit AmpereDefinition of the SI unit AmpereIf two long, parallel wires 1 m apart carry the same current, and the If two long, parallel wires 1 m apart carry the same current, and the magnetic force per unit length on each wire is 2x10magnetic force per unit length on each wire is 2x10-7-7 N/m, then the N/m, then the current is defined to be 1 A.current is