Magnetic Fields and Forces

1. Magnetic Fields and Forces AP Physics C

2. Currents Set up Magnetic Fields • First Right-Hand Rule • Hans Christian Oersted (1777-1851)

3. Right-Hand Rule for Magnetic Fields • x: into the page or away from you • · out of the page or towards you

4. Magnetic Field of a Current Loop:

5. Another look a Magnetic Fields of a Current Loop:

6. Electron as a Magnetic Dipole • The electron spins on its axis, giving rise to a electron current in the direction of rotation.The electron is  like a magnetic dipole, a miniature magnet, with a north end and a south end.

7. Magnetic Spin Dipoles in Iron

8. Dual polarity • Cutting a magnet in halfwill not isolate a singlenorth or south.  One magnet becomes two,then four, and so on. This process will never end; even when the last electron spin dipole is reached, it cannot be cut to reveal a single north or single south pole.

9. Magnetic Fields of a Bar Magnet & the Earth • B-field of bar magnet is similarto the Earth's magnetic field.B-field lines leave north face,enter at south face. • Convection currents insidethe earth set up magnetic field.

10. Bar Magnets • If magnetic dipole loops are oriented the sameon neighboring faces, the magnets attract. • North is attracted to south,and is repelled by north.

11. Compass Needle is a Magnet:   It Aligns with the B-Field    

12. Magnetic Force on Current-Carrying Wire      •  F = ILB sin θThe direction of the force on the wire may be determined by a second  right-hand rule, aright hand rule for magnetic force. • The other right-hand rulegave the direction of themagnetic field B.

13. Using the Right-Hand Rule • To determine the direction of the magnetic force acting on the current-bearing wire

14. Using the RHR: • In which direction, if any, will the metal rod be deflected?

15. Sample Problem • A wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire if the angle between the magnetic field and the current is 60.0 degrees.

16. Sample Problem • A thin, horizontal copper rod 1.0 m long and has a mass of 50 g. What is the minimum current in the rod that will cause it to float in a horizontal magnetic field that is perpendicular to the rod of 2.0 T?

17. Torque on a Current Loop • What is the net force on the current loop? • What is the net torque on the loop?

18. Torque on the Current Loop • At what angle is the torque a maximum value? • At what angle is the torque a minimum value?

19. Sample Problem • A circular loop of radius 2.0 cm contains 50 turns of tightly wound wire. If the current in the windings is 0.30 A and a constant magnetic field of 0.20 T makes an angle of 25 degrees with a vector perpendicular with the loop, what torque acts on the loop?

20. DC Motor

21. Moving Charges in a B-Field: • Electric force can be parallel to direction of velocity, but themagnetic force is always perpendicular to the velocity vector.

22. Magnetic Force on Moving Charges • RHR • F = qvB sin θ

23. Magnetic Force on Moving Charges •  If the velocity v is parallel to the magnetic field B,   the magnetic force is zero because sin θ = 0.

24. Magnetic Force on Moving Charges • What is the direction of the magnetic force on the moving charge in each situation?

25. Magnetic Force on Moving Charges • What is the direction of the force F , if any, in each case?

26. Charges move in a circular path:

27. Circular Paths in Magnetic Fields                                 

28. Circular Motion in B-Field • Right Hand Rule for Force Fingers point in direction of magnetic field B.Thumb points in direction ofthe velocity vector v. • Palm shows the direction of the force F.

29. Mass Spectrometer • F = qvB sin θ • θ  = 90 deg           • F = qvB • F = ma                   • a = v2 /r                 • F = mv2 /r               • qvB = mv2 /r           • m = qBr/v              

30. Sample Problem • A singly charged positive ion moving at 4.6 x 105 m/s leaves a circular track of radius 7.94 mm along a direction perpendicular to the 1.80 T magnetic field of a bubble chamber. Compute the mass (in amus) of this ion, and identify it from that value.

31. Velocity Selector & Mass Spectrometer • In the velocity selector, the E-force and the B-force are equal and opposite, so that, qE = qvB. Therefore, v = E/B. • In 1897, J. J. Thomson used this set-up to determine the mass to charge ratio for electrons.

32. Sample Problem • The electric field between the plates of a velocity selector is 2500 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0350 T. Calculate the radius of the path of a singly charged ion have a mass of 2.18 x 10-28 kg.

33. Electron Beam in a B-Field • Electrons are deflected downward.  What is the  direction of the magnetic field B?

34. Magnetic Flux • Magnetic flux is the product of the average magnetic fieldtimes the perpendicular area that it penetrates.

35. Magnetic Flux Illustrations • The contribution to magnetic flux for a given area is equal to the area times the component of magnetic field perpendicular to the area. For a closed surface, the sum of magnetic flux is always equal to zero (Gauss' law for magnetism).

36. Gauss’s Law for Magnetism • The net magnetic flux out of any closed surface is zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole. The net flux will always be zero for dipole sources.

37. Sample Problem • A cube of edge length 2.50 cm is positioned so that it is position with one corner at the origin, one face in the xy-plane, one face in the yz-plane and one in the xz-plane. A uniform magnetic field given by B = (5.00i +4.00j +3.00k) T exists throughout the region. • Calculate the flux through the face that is parallel to the yz-plane. • What is the total flux through the six faces?