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CHAPTER-28

CHAPTER-28. Magnetic Field. Ch 28-2 What produces a Magnetic Field?. Electric field E produces a electric force F E on a stationary charge q Magnetic field B produces a magnetic force F B on a moving charge q

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CHAPTER-28

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  1. CHAPTER-28 Magnetic Field

  2. Ch 28-2 What produces a Magnetic Field? • Electric field E produces a electric force FE on a stationary charge q • Magnetic field B produces a magnetic force FB on a moving charge q • What produces a Magnetic Field? A Magnetic Monopole? Magnetic monopoles do not exists • Two ways to produce magnetic field B: Electromagnet: magnetic field due to a current Permanent magnet: net magnetic field due to intrinsic magnetic field of electrons in certain material.

  3. Ch 28-3 The Definition of B • Electric field E: E field is tested by measuring force FE on a static charge q E=FE/q • Magnetic Field B is tested by measuring force FB on a moving charge q. If v is charge velocity then FB=q(vxB)=qvBsin • is angle between the v and B. • Direction of B: that direction of V for which FB=0 • Direction of FB:  to plane of V and B

  4. Ch 28-3 The Definition of B • Unit of B Tesla (T): B=FB/qvsin SI unit of magnetic field B (T):Newtons/Coulomb.(m/s) = N/(C/s).m=N/A.m 1T=1N/A.m • Magnetic Field Lines: • B field line starts from N pole ans terminates at S pole • Like magnetic pole repel each other and opposite pole attract each other.

  5. Ch 28-4 Crossed Fields • Crossed fields: a region with E and B field  to each other. If the net force due to these two fields on a charge particle is zero, particle travels undeviated Then FE=FB qE=qvB (=90) E=vB or v=E/B

  6. Ch 28-6 A Circulating Charged Particle • When a charge q moves in a B field then the magnetic force FB=qvBsin=qvB (=90) • For =90 the particle moves in a circular orbit wit a radius given by : FR=FB • mv2/R=|q|vB (m is particle mass) • R=mv/qB or v=|q|RB/m • Particle period T=2R/v • Frequency f=1/T=v/2R • Angular frequency =2f =2f=v/R=|q|B/m If v has a component along B then particle trajectory is a helix (helical path)

  7. Ch 28-8 Magnetic Force on a Current-Carrying Wire • A force is exerted by a magnetic field B on a charge +q moving with velocity v. • Direction of force is same for an electron (-q) moving with velocity vD( in opposite direction to v). • For a wire carrying a current i, number of electrons passing a length of wire L in time t are q-given by : • q-=it=iL/vD & q- =-q and vD=-v • q-=iL/vD reduces to q=iL/v Then FB=q(vxB)= (iL/v)(vxB) FB = i(LxB) FB = iLB

  8. Ch 28-9 Torque on a Current Loop A current carrying rectangular loop placed between the N and S poles of a magnet, no magnetic force on shorter sides but forces in opposite direction on longer sides

  9. Ch 28-9 Torque on a Current Loop Same Magnitude of forces F2 and F4 on shorter sides F2=F4=ibBcos Same Magnitude of forces F1 and F3 on longer sides F1=F3=iaBsin=iaB Net torque due to F1 and F3 is ’ = iaB x (bsin/2) + iaB x (bsin/2) =iabBsin ’ =iABsin= i(AxB)=i

  10. Ch 28-10 Magnetic Dipole Moment • Magnetic moment of a coil: • =NiA ( A is coil area); Then  =  x B =NiAB sin • Torque  exerted on an electric dipole p in an electric field E :  = p x E • Torque due to electric or magnetic field = vector product of dipole moment and field vector • Electric potential energy U() of a electric dipole moment p in an E field U()= -p.E • Magnetic potential energy of a magnetic dipole  U() = -  . B = -  B cos Max. value of U() : for  = 180 Min. value of U() for  =0 Work done by a magnetic field in rotating a a magnetic dipole from initial orientation i to final orientation f W=-U= -(Uf-Ui) Wappl=-W

  11. Suggested problems Chapter 28

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