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24_EquationSheet

24_EquationSheet - Equation Sheet B= o qv r 2 4 |r | E= 1q...

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Equation Sheet v B = μ o 4 π qvV × ˆ r | v r | 2 v E = 1 4 πǫ o q | v r | 2 ˆ r v F = q v E + × v B Other Fundamental Concepts Δ U el = q Δ ± Δ ± = i f i v E d v l ≈ − ( E x Δ x + E y Δ y + E z Δ z ) Φ el = i v E ˆ ndA Φ mag = i v B ˆ ndA c v E ˆ ndA = q inside ǫ 0 c v B ˆ ndA = 0 | emf | = c v E NC d v l = v v v v d Φ mag dt v v v v c v B d v l = μ 0 b I inside path + ǫ 0 d dt i v E ˆ ndA B Specifc Results v E due to uniformly charged spherical shell: outside like point charge; inside zero v v v v E dipole,axis v v v 1 4 πǫ 0 2 qs r 3 (on axis, r s ) v v v v E dipole, v v v 1 4 πǫ 0 qs r 3 (on axis, r s ) v v v v E rod v v v = 1 4 πǫ 0 Q r r r 2 + ( L/ 2) 2 ( r from center) p = qs electric dipole moment v v v v E rod v v v 1 4 πǫ 0 2 Q/L r (if r L ) v v v v E ring v v v = 1 4 πǫ 0 qz ( z 2 + R 2 ) 3 / 2 ( z along axis) v v v v E disk v v v = Q/A 2 ǫ 0 b 1 z ( z 2 + R 2 ) 1 / 2 B ( z along axis) v v v v E disk v v v Q/A 2 ǫ 0 ± 1 z R ² Q/A 2 ǫ 0 (if z R ) v v v
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24_EquationSheet - Equation Sheet B= o qv r 2 4 |r | E= 1q...

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