Magnetic Forces and Fields

Transcription

1 Magnetic Forces and Fields Physics 102 Lecture 3 21 February 2002 IF NOT REGISTERED FOR PHYSICS 102, SEE REGISTRAR ASAP, AND REGISTER 21 Feb 2002 Physics 102 Lecture 3 1

2 RC Puzzler 21 Feb 2002 Physics 102 Lecture 3 2

3 Magnetic Fields Magnetic poles come in two types: North and South, and poles ALWAYS come in pairs. Like poles repel, unlike poles attract. The magnetic field points from N to S; at any point its direction is the direction a compass N pole would point. NB: the north (geomagnetic) pole is a south pole! Like Earth s south geomagnetic pole The nation that controls magnetism will rule the world - Dick Tracy 21 Feb 2002 Physics 102 Lecture 3 3

4 Neutron star Spin period is 0.01 seconds! Has the mass of the 1.4 Suns! Earth 13,000 km 10 km 21 Feb 2002 Physics 102 Lecture 3 4

5 Magnetic Materials Individual atoms have B fields from electron motion and spin In most materials, atomic B fields point in different directions and cancel out In ferromagnetic materials (iron, nickel, etc), regions (domains) have aligned atomic B fields Domains can be induced to line up by applying an external B field 21 Feb 2002 Physics 102 Lecture 3 5

6 Magnetic Force on a Moving Charge Magnetic forces act only on charges MOVING with a component perpendicular to the magnetic field. (Recall F = qe for E) The force is proportional to the perpendicular velocity component sinθ and to the charge. v F = q ( vsinθ )B Force direction is perpendicular to both v and B (right hand rule: thumb in v direction, fingers B, palm F). SI magnetic field unit is the tesla (newtonsecond/coulomb-meter). 10,000 Gauss = 1 Tesla 21 Feb 2002 Physics 102 Lecture 3 6 F q 0 vsinθ 0 θ v B

7 B B B I q 0 q 0 Case I, charge at rest.case II, charge with velocity v. Case III, loop of current carrying wire. In which case(s) is there a net force on the object? A) I and II B) III only C) II and III D) no cases 21 Feb 2002 Physics 102 Lecture 3 7

8 Motion of a charge in a B field 2 F = qvb = mv / r r = mv Which way does the B field point? A) Into the board B) Toward you C) To the right D) Toward the ceiling 21 Feb 2002 Physics 102 Lecture 3 8 qb

9 A. Poles B. Mid-Latitudes C. Equator 21 Feb 2002 Physics 102 Lecture 3 9

10 Force on a Current in a B Field A current is made up of moving charges, hence a B field exerts a force on a wire with a current in it. F = ( ) q vbsinθ q = v tbsinθ t = ILBsinθ Thumb I, fingers B, palm F (right hand rule) When the current is applied, which way will the bar move? Likewise, a loop of wire feels a torque that tends to rotate it so that its normal is aligned with the B field 21 Feb 2002 Physics 102 Lecture 3 10

11 LET S MEASURE A MAGNETIC FIELD I L L = 0.1 m I = 10 A N = 20 turns F = 10 N B F B =? F = NILB (since perpendicular) B = F/NIL = 0.5 Tesla = 5000 Gauss 21 Feb 2002 Physics 102 Lecture 3 11

12 A Simple Motor Brush Force Current out of page Brush Brush B field Current into page Force 21 Feb 2002 Physics 102 Lecture 3 12

13 Ampere s Law For a static current distribution: l = B µ 0I where the sum is over a loop made up of small line segments l and I is the total (net) current through the loop. Here 7 µ 0 = 4π 10 T m/a is the permeability of free space The field around a wire with current I: B l = = µ I B 0 or B = µ I ( 2πr) 0 l = B ( 2πr) 21 Feb 2002 Physics 102 Lecture 3 13

14 Equal currents are running in the same direction in the two wires on the right. A)The magnetic field from the left wire cancels the field from the right wire at the position of the right wire. B) The wires are attracted to each other. C)The wires repel each other. D) The net forces from each other must cancel. (Otherwise wires would move whenever we put a current through them.) I I 21 Feb 2002 Physics 102 Lecture 3 14

15 B Field Produced by Moving Charges Experimentally, a wire with a current flowing in it produces a magnetic field µ 0I B = where the 2πr If the right thumb points in the direction of I, then the fingers curl in the direction of B (right hand rule #2) Two parallel wires with currents in the same direction attract each other; in the opposite direction they repel each other. I F wire 1 wire 2 F B from 1 21 Feb 2002 Physics 102 Lecture 3 15

16 B Fields in Loops and Coils A loop of wire with N turns has a B field (at the center): B = N µ 0 I 2R A solenoid is a coil wound in a helix. If there are n=n/l turns per unit length, the field inside is uniform and given by B = µ 0nI 21 Feb 2002 Physics 102 Lecture 3 16

17 What makes magnetism on the atomic scale? (1)Electrons orbiting the nucleus (2)Electrons spinning on their own axes These effects produce microscopic magnetic dipoles Magnetism could not be understood until quantum mechanics was discovered. on the nuclear scale... The quarks that make up proton orbit within the proton and create nuclear magnetic dipoles. Thus protons spin and posses a magnetic dipole. The technique of MRI (Magnetic Resonance Imaging) maps out the precessions of nuclear dipoles. The precession depends on the environment. 21 Feb 2002 Physics 102 Lecture 3 17