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(see fig 8-3hw). We wish to determine the field at P due to the charges on the rod. Because the rod is centered at the origin, symmetry tells us the electric field at P must point in the direction. Based on the differ- ential form dErk- determine the integrated expression for E, at P. kQ 1. {Hint: use the math identity dy/p² = da/r. This identity can be derived using the geo- metric relation tana = r/(-y) (1), and the calculus identity d tan a/da = sec² a = p²/y² (2).} 2. 3. 4. 16 56 515-15-15 6. kQ kQ Lr -(cosa2 - cosa₁) kQ (Qdy/L) p² kQ -(cos α2 Lr T (cos a2- cos a₁) kQ L (cosa₁ - cos a₂) - 5. -(cosa₁ - cos α₂) cos 01) sina, -(cos α₁ - cos a₂)

(see fig 8-3hw). We wish to determine the field at P due to the charges on the rod. Because the rod is centered at the origin, symmetry tells us the electric field at P must point in the direction. Based on the differ- ential form dErk- determine the integrated expression for E, at P. kQ 1. {Hint: use the math identity dy/p² = da/r. This identity can be derived using the geo- metric relation tana = r/(-y) (1), and the calculus identity d tan a/da = sec² a = p²/y² (2).} 2. 3. 4. 16 56 515-15-15 6. kQ kQ Lr -(cosa2 - cosa₁) kQ (Qdy/L) p² kQ -(cos α2 Lr T (cos a2- cos a₁) kQ L (cosa₁ - cos a₂) - 5. -(cosa₁ - cos α₂) cos 01) sina, -(cos α₁ - cos a₂)

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L/2. 0 Ay I - L/2 02 a α1 T P ΔΕ Ρ ΔΕ, Consider a uniformly charged thin rod with total charge Q and length L. It is aligned along the y-axis and centered at the origin
Transcribed Image Text:L/2. 0 Ay I - L/2 02 a α1 T P ΔΕ Ρ ΔΕ, Consider a uniformly charged thin rod with total charge Q and length L. It is aligned along the y-axis and centered at the origin
(see fig 8-3hw). We wish to determine the field at P due to the charges on the rod. Because the rod is centered at the origin, symmetry tells us the electric field at P must point in the direction. Based on the differ- ential form dEr = k- sin a, determine the integrated expression for E, at P. {Hint: use the math identity dy/p² = da/r. This identity can be derived using the geo- metric relation tan a = r/(-y) (1), and the calculus identity d tan a/da= sec² a = sec² a = p²/y² (2).} kQ 1. (cos α2 - cos α₁) L kQ 2. 3. 4. 5. (Qdy/L) p² 6. T kQ Lr kQ Lr kQ T kQ L (cos α₂ - cos α₁) (cosa₁ - cos a₂) (cos a 2 - cosa₁) (cos α₁ - cos α2) (cosa₁ - cos a2)
Transcribed Image Text:(see fig 8-3hw). We wish to determine the field at P due to the charges on the rod. Because the rod is centered at the origin, symmetry tells us the electric field at P must point in the direction. Based on the differ- ential form dEr = k- sin a, determine the integrated expression for E, at P. {Hint: use the math identity dy/p² = da/r. This identity can be derived using the geo- metric relation tan a = r/(-y) (1), and the calculus identity d tan a/da= sec² a = sec² a = p²/y² (2).} kQ 1. (cos α2 - cos α₁) L kQ 2. 3. 4. 5. (Qdy/L) p² 6. T kQ Lr kQ Lr kQ T kQ L (cos α₂ - cos α₁) (cosa₁ - cos a₂) (cos a 2 - cosa₁) (cos α₁ - cos α2) (cosa₁ - cos a2)
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