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TOPIC 8 Magnetic Fields

TOPIC 8 Magnetic Fields. Permanent Magnets. Some metals, such as iron and nickel, may be natural magnets. They have north and south poles (near ends). Unlike poles attract; like poles repel. North pole of magnet points towards North.

quentin-briggs
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TOPIC 8 Magnetic Fields

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  1. TOPIC 8Magnetic Fields

  2. Permanent Magnets • Some metals, such as iron and nickel, may be natural magnets. • They have north and south poles (near ends). • Unlike poles attract; like poles repel. • North pole of magnet points towards North. • Earth acts like giant magnet – with magnetic south pole near geographic North!! • Breaking bar magnet does not givefree N or S pole. • Even at subatomic level, there is noevidence for magnetic monopoles.

  3. Magnetic Fields • Forces between poles without contact – “action at a distance” (like Coulomb’s law for charge). • Magnetic field, B. • SI unit of B is Tesla (T) – large value • Smaller unit is Gauss – 1 G = 10–4 T • Earth’s field ~0.5 G • Lack of free poles mean can’t define field by “force on a unit magnetic pole”. • Moving charges experience magnetic effects • Create magnetic fields (see later) • Feel force due to external magnetic fields

  4. Force on Moving Charge • Magnetic force on moving charge is • Proportional to magnitude of charge • Proportional to speed of charge • Perpendicular to direction of magnetic field • Perpendicular to velocity • Where  is angle between v and B • Does no work on charge – no change in K.E.

  5. Motion of Charge in B field • (Convention for vectors into () andout of () plane of drawing) • Consider initial velocity perpendicularto B • Force always perpendicular to v • No change in magnitude of v. • Circular motion, centripetal force • Spectrometers, cyclotrons etc

  6. Example 1 A proton moves in a circular orbit of radius 2.5 cm in a uniform magnetic field of 0.8 T, perpendicular to the velocity of the proton. What is the speed of the proton? How long does it take it to execute one complete turn of the orbit?

  7. Electric & Magnetic Forces • Combined electric & magnetic fields acting on charged particle produce Lorentz force • Special case – crossed E and B fields • (a) if qE = –qvB, no net force • Selects • (b) v < v0: electrostatic force predominant • (c) v > v0 : magnetic force predominant

  8. Force on Electric Current • Wire length , area A, with n carriers/unit volume • Equivalent to charge Q = n q A. • Drift velocity vd • Force = q v BF = n q A vdB • But I = n q A vd • Therefore F = I B, or • Note:force is perpendicular to both  and B. • If wire not straight, or field not uniform • Then integrate over current elements.

  9. Example 2 A wire is bent into a semicircular loop of radius R. It carries a current I, and its plane is perpendicular to a uniform magnetic field B. What is the magnitude and direction of the force on the loop?

  10. Current Loops and Magnetic Dipoles • Continuous loop in uniform field  equal forces to left and right etc. • No net force. • Forces not necessarily along same line  torque. • Consider planar loop, inclined to magnetic field. • Forces on ends exactly balance. • Forces on front and back F = I b B • These are not aligned, soproduce a torque.

  11. Current Loops and Magnetic Dipoles • Perpendicular distance between lines of forces = a sin . • Torque  = Fa sin  = Iab B sin  • Define dipole moment of coilof area A by  = I A . •  =  B sin  • Vector equation Edge view • Sign of  defined by right hand rule:fingers pointing in current direction, thumb indicates direction of .

  12. Potential Energy of Magnetic Dipole • Torque tends to align dipole with magnetic field. • Rotating back against forces gives dipole potential energy • Define U = 0 when plane of coil is parallel to magnetic field(ie dipole is perpendicular to field) • (Note similarity with electric dipoles in electric field E)

  13. Example 3 A rectangular coil consists of 25 turns of wire of dimensions 5.4 cm by 8.5 cm, and carries a current of 15 mA. A magnetic field of 0.35 T is applied parallel to the plane of the loop. (a) Find the magnitude of the dipole moment of the coil. (b) Calculate the magnitude of the torque acting on the loop. (c) If the coil is allowed to turn under the action of the torque until it reaches its equilibrium position, what will be the change in its potential energy?

  14. Hall Effect • Consider strip of conductor, perpendicular to B field. • When current flows, carriers feel force perpendicular to B and current. • Charge builds up alongedges of conductor. • Causes electric field,opposing magneticforce. • Potential difference between edges known as Hall voltage. • Used to measure B (or n).

  15. Example 4 A current of 8 A flows through a ribbon of copper foil, of thickness 10 m, which is perpendicular to a magnetic field of 2 T. If the charge carrier density in copper is 8.51028 m–3, calculate the Hall voltage which will be developed across the ribbon.

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