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Magnetism

Magnetism. Magnetic Fields . Magnetic dipoles cause space to be modified in their vicinity. They form a “magnetic field”. The magnetic field caused by magnetic “poles” is analogous to the electric field caused by electric “poles” or “charges”. N. S. Magnetic Field, B. More Magnetic Fields.

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Magnetism

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  1. Magnetism

  2. Magnetic Fields • Magnetic dipoles cause space to be modified in their vicinity. • They form a “magnetic field”. • The magnetic field caused by magnetic “poles” is analogous to the electric field caused by electric “poles” or “charges”.

  3. N S MagneticField, B

  4. More Magnetic Fields

  5. Compasses • If they are allowed to select their own orientation, magnets align so that the north pole points in the direction of the magnetic field. • Compasses are magnets that can easily rotate so that they can align themselves to a magnetic field. • The north pole of the compass points in the direction of the magnetic field.

  6. Sample Problem • We say that a compass points to the Earth’s North Magnetic Pole (which is near the North Pole). • Is the North Magnetic Pole the north pole of the Earth’s Magnetic Field?

  7. Magnetic “Monopoles” • Do not exist! • In this way, magnetic poles differ from electric poles (charges), which can be separated into electric monopoles.

  8. Units of Magnetic Field • Tesla (SI) • N/(C m/s) • N/(A m) • Gauss • 1 Tesla = 104 gauss

  9. Magnetic Force on Particles • Magnetic fields cause the existence of magnetic forces. • A magnetic force is exerted on a particle within a magnetic field only if • the particle has a charge. • the charged particle is moving with at least a portion of its velocity perpendicular to the magnetic field.

  10. Magnetic Force on a Charged Particle • magnitude: F = qvBsin • q: charge in Coulombs • v: speed in meters/second • B: magnetic field in Tesla • : angle between v and B • direction: Right Hand Rule • FB = q v x B (This is a “vector cross product”)

  11. The Right Hand rule to Determine a Vector Cross Product • Align your hand along the first vector. • Orient your wrist so that you can “cross” your hand into the second vector. • Your thumb gives you the direction of the third vector (which is the result).

  12. Sample Problem #1 Calculate the magnitude force exerted on a 3.0 mC charge moving north at 300,000 m/s in a magnetic field of 200 mT if the field is directed • North. • South. • East. • West.

  13. Sample Problem #2 • Calculate the magnitude and direction of the magnetic force. v = 300,000 m/s 34o q = 3.0mC B = 200 mT

  14. Magnetic forces… • are always orthogonal (at right angles) to the plane established by the velocity and magnetic field vectors. • can accelerate charged particles by changing their direction. • can cause charged particles to move in circular or helical paths.

  15. Magnetic forces cannot... • change the speed or kinetic energy of charged particles. • do work on charged particles.

  16. Magnetic Forces… • …are centripetal. • Remember that centripetal acceleration is v2/r. • Remember centripetal force is therefore mv2/r.

  17. V F V F F F V V Magnetic Forces are Centripetal SF = ma FB = Fc qvBsin = mv2/r qB = mv/r q/m = v/(rB) B

  18. Sample Problem #3 What is the orbital radius of a proton moving at 20,000 m/s perpendicular to a 40 T magnetic field?

  19. Sample Problem #4 What must be the speed of an electron if it is to have the same orbital radius as the proton in the magnetic field described in the previous problem?

  20. Sample Problem An electric field of 2000 N/C is directed to the south. A proton is traveling at 300,000 m/s to the west. What is the magnitude and direction of the force on the proton? Describe the path of the proton? Ignore gravitational effects.

  21. Sample Problem A magnetic field of 2000 mT is directed to the south. A proton is traveling at 300,000 m/s to the west. What is the magnitude and direction of the force on the proton? Describe the path of the proton? Ignore gravitational effects.

  22. e- 300,000 m/s E = 2000 N/C Sample Problem • Calculate the force and describe the path of this electron.

  23. e- 300,000 m/s Sample Problem • Calculate the force and describe the path of this electron. B = 2000 mT

  24. Sample problem • How would you arrange a magnetic field and an electric field so that a charged particle of velocity v would pass straight through without deflection?

  25. B E Electric and Magnetic Fields Together e- v = E/B

  26. Sample Problem It is found that protons traveling at 20,000 m/s pass undeflected through the velocity filter below. What is the magnitude and direction of the magnetic field between the plates? 20,000 m/s e 0.02 m 400 V

  27. Magnetic Force on Current-Carrying Wire • F = I L B sin • I: current in Amps • L: length in meters • B: magnetic field in Tesla • : angle between current and field

  28. Sample Problem What is the force on a 100 m long wire bearing a 30 A current flowing north if the wire is in a downward-directed magnetic field of 400 mT?

  29. Sample Problem What is the magnetic field strength if the current in the wire is 15 A and the force is downward and has a magnitude of 40 N/m? What is the direction of the current?

  30. N I S Lab: Magnetic Field Map • Using a compass, map the magnetic field inside and outside your solenoid. Do the following: • Put together 4 sheets of graph paper. Write all group members’ names on paper. • Trace the solenoid (true size) • Draw the Compass Rose • Connect to DC outlet • Map magnetic field lines with compass • Draw North and South Poles of solenoid • Extend field lines through solenoid.

  31. Magnetic Fields… • Affect moving charge • F = qvBsinq • F = ILBsinq • Hand rule is used to determine direction of this force. • Caused by moving charge!

  32. Magnetic Field forLong Straight Wire • B = oI / (2r) • o: 4  10-7 T m / A • magnetic permeability of free space • I: current (A) • r: radial distance from center of wire (m)

  33. r  • Right Hand Rule for straight currents i • Curve your fingers • Place your thumb (which is presumably pretty straight) in direction of current. • Curved fingers represent curve of magnetic field. • Field vector at any point is tangent to field line.

  34. I For straight currents

  35. Sample Problem • What is the magnitude and direction of the magnetic field at point P, which is 3.0 m away from a wire bearing a 13.0 Amp current? P 3.0 m I = 13.0 A

  36. Sample Problem – not in packet • What is the magnitude and direction of the force exerted on a 100 m long wire that passes through point P which bears a current of 50 amps in the same direction? I2 = 50.0 A P 3.0 m I1 = 13.0 A

  37. Principle of Superposition • When there are two or more currents forming a magnetic field, calculate B due to each current separately and then add them together using vector addition.

  38. Sample Problem • What is the magnitude and direction of the electric field at point P if there are two wires producing a magnetic field at this point? I = 10.0 A 4.0 m P 3.0 m I = 13.0 A

  39. Sample Problem • Where is the magnetic field zero? I = 10.0 A 7.0 m I = 13.0 A

  40. N B I S In the 4th Grade • You learned that coils with current in them make magnetic fields. • The iron nail was not necessary to cause the field; it merely intensified it.

  41. Solenoid • A solenoid is a coil of wire. • When current runs through the wire, it causes the coil to become an “electromagnet”. • Air-core solenoids have nothing inside of them. • Iron-core solenoids are filled with iron to intensify the magnetic field.

  42. Magnetic Field Inside aSolenoid • B = on I • o: 4  10-7 T m / A • n: number of coils per unit length • I: current (A) • You are not required to memorize this formula, but only to use it.

  43. Magnetic Field around Curved Current B

  44. Right Hand Rule for magnetic fields around curved wires • Curve your fingers. • Place them along wire loop so that your fingers point in direction of current. • Your thumb gives the direction of the magnetic field in the center of the loop, where it is straight. • Field lines curve around and make complete loops. B I

  45. Sample Problem An air-core 10 cm long is wrapped with copper wire that is 0.1 mm in diameter. What must the current be through the wire if a magnetic field of 20 mT is to be produced inside the solenoid?

  46. Sample Problem What is the direction of the magnetic field produced by the current I at A? At B? I A B

  47. Magnetic Field around Curved Current B

  48. Sample Problem What is the magnetic field inside the air-core solenoid shown if the resistance of the copper wire is assumed to be negligible? There are 100 windings per cm. Identify the north pole. 120 V I 100-W

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