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Phy b9 3-1
- 1. 第9章 稳恒磁场 §9.1 磁场 磁感应强度 §9.2 毕奥-萨伐尔定律 磁高斯定理 §9.3 安培环路定理 §9.4 带电粒子在磁场中的运动 §9.5 磁场对载流导线的作用 §9.6 电磁场的相对论性变换
- 2. Magnetic forces on currents §9.5 磁场对载流导线的作用 B r v r lId r S θ Bvqf rrr ×=a charge carrier： 在电流元的范围内外磁场 的值相同B r 磁场对载流导线的作用实际上是载流导线中作定向运动的 大量自由载流子受到洛伦兹力的宏观表现 )( BvqnSdlFd rrr ×=lId r vnqJ rr = SJI = )( BJSdlFd rrr ×= BlId rr ×= Jld rr // BlIdFd rrr ×= 安培力 Ampère force 退出返回
- 3. BlIdFd rrr ×= Ampère force 安培力 ∫ ×= L BlIdF rrr Magnetic force on finite wire with current 3 0 4 r rlId Bd rr r × = π µ 2 12 1211220 12 )( 4 r rˆldIldI Fd ×× = rr r π µ Ampère Law 退出返回
- 4. )()( iˆjˆBdlI ×= ∫−= L dl)kˆ(IB kˆIBLF θsin−= r kˆIBLF −= r finite wire with current BlIdFd rrr ×= 返回 退出 )(( iˆB)jˆdlIFd ×= r )()( kˆBdlI −= ∫ −= L kˆdlBIF )( r )(sin)( kˆBdlIFd −= θ r
- 5. uniform magnetic field A half-circle wire of radius R carries a current I. The wire is placed in a uniform magnetic field. The angle between the path from one end a to another end b of the wire and the magnetic field is α=30 o . What is the magnetic force on the wire? infinitesimal wire with current B r a b lId r I lId r Rab 2= α ∫ ×= ab BlIdF rrr BldI ab rr ×⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ∫ BabI r ×= direction： F r ⊗αsinBabIF = r IBR= 退出返回
- 6. A long straight wire passes through the centre of circular flat loop of wire vertically, both carrying current I. what is the interactive force? BlIdFd infinitesimal wire with current rrr ×= 0=F r 0=× BlId rr lId r ∫ ×= L BlIdF rrr An arbitrarily shape flat loop of wire, carrying current I, is placed in a uniform magnetic field. ∫ ×= L BlIdF rrr BldI L rr ×⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ∫ 0= I I Idl 返回 退出
- 7. Magnetic force on current loops A rectangular loop of wire, carrying a current and free to rotate about a fixed axis, is placed in a magnetic field. Magnetic forces on the wire produce a torque that rotates it. 退出返回
- 8. a b θsin31 BIaFF == BIbFF == 42 ϕϕ sin 2 sin 2 22 F a F a M += N turns NISm mB NBISM = = = ϕ ϕ sin sin BmM rrr ×= 0=F r nˆ ϕ ϕ θ 返回 退出 ϕsinBIS=ϕsinBIba= ϕsinmB=
- 9. An arbitrary shape flat loop of wire , carrying current I through uniform magnetic field. 0=F r I Infinitesimal rectangular loops of wire, carrying current I BmdMd rrr ×=nˆIdSmd = r ∫∫ ×== )( BmdMdM rrrr BmM rrr ×= )( BnˆIdS r ×= ∫ BnˆdSI r ×= ∫ )( Bm rr ×=BnˆIS r ×= 退出返回
- 10. CAI 退出返回