physics 112N magnetic fields and forces

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1 physics 112N magnetic fields and forces

2 bar magnet & iron filings physics 112N 2

3 bar magnets physics 112N 3

4 the Earth s magnetic field physics 112N 4

5 electro -magnetism! is there a connection between electricity and magnetism?! place a compass near a current carrying wire physics 112N 5

6 electro -magnetism! is there a connection between electricity and magnetism?! a loop carrying a large current physics 112N 6

7 magnetic fields! a vector at each point in space! compasses line up along these vectors! will produce a force on any moving charge (more later) physics 112N 7

8 magnetic fields! a vector at each point in space! compasses line up along these vectors! will produce a force on any moving charge (more later) physics 112N 8

9 magnetic fields physics 112N 9

10 magnetic fields! a vector at each point in space! compasses line up along these vectors! will produce a force on any moving charge (more later) physics 112N 10

11 magnetic fields physics 112N 11

12 magnetic fields physics 112N 12

13 magnetic field superposition! just as the total electric field at any point is the vector sum of the fields from all charges nearby,! so the total magnetic field is the vector sum of the fields from all magnetic sources nearby.! Consider two solenoids producing nearly uniform fields: physics 112N 13

14 magnetic field superposition physics 112N 16

15 magnetic forces! magnetic fields produce a force on charged particles that are moving through them! experiments show that the strength of the force is proportional to the charge the speed of the particle the magnitude of the magnetic field! experiments also show the direction the force acts in perpendicular to the velocity perpendicular to the magnetic field physics 112N 17

16 magnetic forces - the right-hand rule physics 112N 18

17 magnetic forces - the right-hand rule physics 112N 19

18 proton beam through a magnetic field A beam of protons moves through a uniform magnetic field with magnitude 2.0 T, directed along the positive z-axis. The protons have a velocity of magnitude 3.0x10 5 m/s in the xz-plane at an angle of 30 o to the positive z-axis. Find the magnitude and direction of force on the proton. physics 112N 21

19 motion of charged particles in a magnetic field consider a positive charge moving in a plane perpendicular to a uniform magnetic field force is always perpendicular to the velocity and is of constant magnitude constant acceleration perpendicular to the velocity circular motion radius of the circle determined by physics 112N 25

20 protons in a magnetic field A beam of protons traveling at 1.20 km/s enters a uniform magnetic field traveling perpendicular to the field. The beam exits the magnetic field in a direction perpendicular to its original direction. The beam travels a distance of 1.18 cm in the field. What is the magnitude of the magnetic field? proton path physics 112N 27

21 force on a current carrying conductor! what happens if we put a wire carrying current into a magnetic field?! it contains moving charges, so we d guess it feels a force we can work out a formula for the force: force on each charge in time Δt, a charge Q = I Δt flows in in time Δt, a charge moves so the total charge in the rod is the total force on the rod is physics 112N 28

22 force on a current carrying conductor! if the magnetic field is not perpendicular to the wire, then the formula is modified! only the perpendicular component of the B-field contributes to the force physics 112N 29

23 force and torque on a current loop! what happens if we put a closed current loop into a magnetic field? e.g. consider a rectangular current carrying loop of wire in a uniform field physics 112N 31

24 force and torque on a current loop! what happens if we put a closed current loop into a magnetic field? e.g. consider a rectangular current carrying loop of wire in a uniform field z x physics 112N 32

25 force and torque on a current loop! what happens if we put a closed current loop into a magnetic field? e.g. consider a rectangular current carrying loop of wire in a uniform field z x loop feels a torque physics 112N 33

26 force and torque on a current loop! what happens if we put a closed current loop into a magnetic field? e.g. consider a rectangular current carrying loop of wire in a uniform field z x physics 112N 34

27 force and torque on a current loop! what happens if we put a closed current loop into a magnetic field? e.g. consider a rectangular current carrying loop of wire in a uniform field z x physics 112N 35

28 force and torque on a current loop! what happens if we put a closed current loop into a magnetic field? e.g. consider a rectangular current carrying loop of wire in a uniform field N.B. the animation isn t showing the actual motion caused by the torque, just the variation of force with angle physics 112N 36

29 solenoid in a uniform field! the torque on the solenoid tends to line it up along the field! same thing that a bar magnet does physics 112N 40

30 magnetic field from a long straight wire We now know what happens to moving charges and current carrying wires in magnetic fields! but how do we generate a magnetic field?! turns out we can generate magnetic fields using electrical currents! simplest example is a long, straight current-carrying wire magnitude of field a perpendicular distance r from a wire carrying current I permeability of vacuum μ0 = 4!"10-7 Tm/A (magnetic analogue of ε0) physics 112N 41

31 magnetic field from a long straight wire physics 112N 42

32 solenoid field strength inside the coil n = turns per unit length physics 112N 45

33 typical field strengths typical field strength from a wire 1 cm away from a wire carrying 10 A, B ~ 10-4 T ~ 1 Gauss typical field strength in a solenoid 200 turns in 10cm length carrying 10 A B ~ 10-2 T ~ 10 Gauss a strong fridge magnet Earth s magnetic field close to the pole, B ~ 10-1 T ~ 100 Gauss B ~ 5!10-5 T ~ 0.5 Gauss electromagnet with an iron core B ~ 1 T ~ 10 4 Gauss superconducting electromagnets (e.g. in the LHC) B ~ 10 T ~ 10 5 Gauss physics 112N 47

Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

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