31-33. Electric Field of Charged Rod

31-33. Electric Field of Charged Rod - Electric Field of...

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Electric Field of Charged Rod (1) Charge per unit length: λ = Q/L Charge on slice dx : dq = λdx x L dE y x dq = λ dx ++ +++ +++ ++ + + D Electric field generated by slice dx : dE = kdq x 2 = kλdx x 2 Electric field generated by charged rod: E = Z D + L D dx x 2 = » 1 x D + L D = » 1 D 1 D + L = kQ D ( D + L ) Limiting case of very short rod ( L D ) : E kQ D 2 Limiting case of very long rod ( L D ) : E D 28/1/2008 [tsl31 – 1/3]
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Electric Field of Charged Rod (2) Charge per unit length: λ = Q/L Charge on slice dx s : dq = λdx s Trigonometric relations: y p = r sin θ, x s = r cos θ x s = y p cot θ, dx s = y p sin 2 θ dE = kλdx s r 2 = kλdx s y 2 p sin 2 θ = kλdθ y p dE y = dE sin θ = y p sin θdθ E y = y p Z θ 2 θ 1 sin θdθ = y p (cos θ 2 cos θ 1 ) dE x = dE cos θ = y p cos θdθ E x = y p Z θ 2 θ 1 cos θdθ = y p (sin θ 2 sin θ 1 ) 28/1/2008 [tsl32 – 2/3]
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31-33. Electric Field of Charged Rod - Electric Field of...

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