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Electricity & Magnetism

Electricity & Magnetism. Magnetism & Electromagnetism. Magnets and Magnetic Fields. Magnets form a magnetic field around them, caused by magnetic “poles.” These are similar to electric “poles” or “charge.”

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Electricity & Magnetism

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  1. Electricity & Magnetism Magnetism & Electromagnetism

  2. Magnets and Magnetic Fields Magnets form a magnetic field around them, caused by magnetic “poles.” These are similar to electric “poles” or “charge.” Magnetic field lines leave the magnet from the north pole and reenter into the south pole

  3. Magnetic Fields Magnetic field lines are continuous field lines in loops with no beginning or end (not like electric field lines The symbol for a magnetic field is B

  4. 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 and align themselves

  5. Practice Problem #1 A compass points to the Earth’s North magnetic pole (which is near the north geographic pole) Is the North Magnetic Pole the north pole of the Earth’s Magnetic field?

  6. Magnetic Monopoles • Magnetic Monopoles DO NOT EXIST!!! • Magnetic poles cannot be separated from each other in the same way that electric poles (charges) can be • Electric monopoles exist as either a negatively charged object or a positively charged object

  7. Magnetic Fields • Units: • Tesla (SI unit) • N/(C m/s) • N/(A m) • Gauss • 1 Tesla = 104 gauss

  8. Magnetic Force • Magnetic fields cause the existence of magnetic forces like electric fields cause electric 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

  9. Magnetic Force on a Charge • Magnitude: F = qvBsinΘ • q = charge in Coulombs (C) • v = velocity in m/s • B = magnetic field in Tesla • Θ = angle between v and B • Direction: Right hand rule if q is positive, left hand rule if q is negative • FB = q v x B (This is a “vector cross product” for those of you who know your math)

  10. Direction of the magnetic force? Right Hand Rule To determine the DIRECTION of the force on a POSITIVE charge we use a special technique that helps us understand the 3D/perpendicular nature of magnetic fields. Basically you hold your right hand flat with your thumb perpendicular to the rest of your fingers • The Fingers = Direction B-Field • The Thumb = Direction of velocity • The Palm = Direction of the Force For NEGATIVE charges use left hand!

  11. Practice #2 • Calculate the magnitude of the force on a 3.0 C charge moving north at 300,000 m/s in a magnetic field of 200 mT if the field is directed • North • East • South • West

  12. Sample Problem: • Calculate the magnitude of force exerted on a 3.0 μC charge moving north at 300,000 m/s in a magnetic field of 200 mT if the field is directed a)N, b)E, c)S, d)W a) F = qvBsinθ F = 3x10-6C ·3x105m/s ∙ 0.2T ∙ sin0o = 0 N b) F = qvBsinθ F = 3x10-6C ·3x105m/s ∙ 0.2T ∙ sin90o = 0.18 N c) F = qvBsinθ F = 3x10-6C ·3x105m/s ∙ 0.2T ∙ sin180o = 0 N d) F = qvBsinθ = -0.18 N F = 3x10-6C ·3x105m/s ∙ 0.2T ∙ sin270o

  13. Practice #3 Calculate the magnitude and direction of the magnetic force

  14. v = 300,000 m/s 34o B = 200 mT q = 3.0μC F = qvBsinθ F = 3x10-6C ∙ 300000 m/s ∙ 0.2T ∙ sin(34o) F =0.101N upward Calculate the magnitude and direction of the magnetic force.

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

  16. Magnetic Forces Magnetic Forces CANNOT change the speed or KE of charged particles Magnetic Forces CANNOT do work on charged particles (F is perpendicular)

  17. Magnetic Forces • Magnetic forces ARE centripetal • Remember centripetal acceleration is v2/r • Centripetal force is mv2/r

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

  19. Practice #4 What is the orbital radius of a proton moving at 20,000 m/s perpendicular to a 40 T magnetic field?

  20. Magnetic Forces on Charged Particles … • …are centripetal. • Remember centripetal force is mv2/r. • For a charged particle moving perpendicular to a magnetic field • F = qvB = mv2/r • Radius of curvature of the particle • r = mv2/qvB = mv/qB

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

  22. Practice #5 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?

  23. Sample Problem 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?

  24. 6. An electric field of 2,000 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.

  25. 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.

  26. 7 A magnetic field of 2,000 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.

  27. 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.

  28. 8 Calculate the force and describe the path of this electron if the electric field strength is 2000 N/C

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

  30. 10 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?

  31. Electric and Magnetic Fields Together

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

  33. 11 e+ 0.02 m 400 V It is found that protons when traveling at 20,000 m/s pass undeflected through the velocity filter below. What is the magnetic field between the plates?

  34. 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

  35. Magnetic Force on Current-Carrying Wires • F = I L B sin Θ • I = current in Amps • L = length in m • B = magnetic field in Tesla • Θ = angle between current and B field

  36. 12 What is the force on a 100m long wire bearing a 30A current flowing north if the wire is in a downward-directed magnetic field of 400 mT?

  37. 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?

  38. 13 What is the magnetic field strength if the current in the wire is 15 A and the force is downward with a magnitude of 40 N/m? What is the direction of the current?

  39. 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?

  40. Magnetic Fields • Magnetic Fields affect moving charge • F = qvBsinΘ • F = ILBsin Θ • Magnetic fields are caused by moving charge

  41. Magnetic Field for a Long Straight Wire • B = 0I/(2πr) • 0 : 4 π x 10-7 T m/A • Magnetic permeability of free space • I: current (A) • R: radial distance from center of wire (m)

  42. Right Hand Rule for straight currents Curve your fingers Place your thumb in the direction of the current Curved fingers represent the curve of the magnetic field Field vector at any point is tangent to the field line

  43. 14 What is the magnitude and direction of the magnetic field at P, which is 3.0 m away from a wire bearing a 13.0 A current?

  44. 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

  45. 15 P I2 = 50.0 A 3.0 m I1 = 13.0 A 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?

  46. 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

  47. Principle of Superposition Remember this from electrostatics? 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.

  48. 16 I2 = 10.0 A 4.0 m P 3.0 m I1 = 13.0 A 16. 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?

  49. 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

  50. Way back in elementary school… You learned that coils with current in them make magnetic fields (electromagnets) The iron nail was not necessary to cause the field, it only intensified it

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