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lecture13 - 8 Magnetic field of moving charge 1 What is the...

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8. Magnetic field of moving charge 2 0 sin 4 r v q B θ π μ = 2 0 4 r r v q B × = π μ 4) For v<<c and a=0 : 1) What is the problem with moving charge? 2) For v=0 and a=0 : r r r q k E 2 = (Coulomb’s law) 0 = B 3) For v=0 and a=0 : ( 29 ( 29 ( 29 c v r r c v r r c v kq E - - - = 3 2 2 1 ( 29 ( 29 ( 29 ( 29 r v c v r r c v c kq c E r B × - - = × = 3 2 2 2 1 0 4 1 πε = k 0 0 2 1 μ ε = c Speed of light:
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Example (two moving protons with v<<c and a=0 ) j r q F E ˆ 4 1 2 2 0 2 πε = x y z 2 v r B + 1 v + E F B F ( 29 k r qv r j i v q r r v q B ˆ 4 ˆ ˆ 4 4 2 0 2 0 2 1 0 1 π μ π μ π μ = × = × = ( 29 j r v q k r qv i v q B v q F B ˆ 4 ˆ 4 ˆ 2 2 2 0 2 0 1 2 π μ π μ = × - = × = i v v v ˆ 2 1 = - = Given:
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9. Bio-Savart law 2 0 4 r r l Id B d × = π μ 2 0 2 0 4 4 r r v Nq B B r r v q B d tot × = = × = π μ π μ × = 2 0 4 r r l Id B π μ l A lA N n nlA N d d v l v l = d v I nqAv d = 2 0 4 r r v nlA B × = π μ 2 0 sin 4 r Idl dB θ π μ = B v d and between angle - θ = 2 0 sin 4 r Idl B θ π μ
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8. Applications of Bio-Savart law 1) Magnetic field of a straight current ( 29 - - + = = a a a a y x xdy I r Idl B 2 / 3 2 2 0 2 0 4 sin 4 π μ θ π μ 2 2 0 2 4 a x x a I B + = π μ x I B a π
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