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L/2 0 Ay -L/2 y 02 Q α1 T P ΔΕ P ΔΕ, (Qdy/L) p² Consider a uniformly charged thin rod with total charge 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. 2 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 sina, dEr = k- 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 tana = r/(-y) (1), and the calculus identity d tan a/da = sec² a = p²/y² (2).} 1. 2. 3. kQ L 5. -(cosa2 - cos α₁) kQ T -(cos a2 - cosa₁) kQ Lr -(cos α₁ - cosa₂) kQ 4. -(cos α2 - cos α₁) Lr kQ T -(cos α₁ - cos a₂) kQ L (cos α₁ - cos a2)

L/2 0 Ay -L/2 y 02 Q α1 T P ΔΕ P ΔΕ, (Qdy/L) p² Consider a uniformly charged thin rod with total charge 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. 2 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 sina, dEr = k- 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 tana = r/(-y) (1), and the calculus identity d tan a/da = sec² a = p²/y² (2).} 1. 2. 3. kQ L 5. -(cosa2 - cos α₁) kQ T -(cos a2 - cosa₁) kQ Lr -(cos α₁ - cosa₂) kQ 4. -(cos α2 - cos α₁) Lr kQ T -(cos α₁ - cos a₂) kQ L (cos α₁ - cos a2)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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L/2 0 Ay -L/2 02 a α1 T P ΔΕ (Qdy/L) p² ΔΕ, Z 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 = =p²/y² (2).} 1. (cos α2 - cos α₁) kQ L 2. 4. kQ 3. -(cos α₁ - cos α₂) Lr 5. kQ r 6. kQ Lr kQ r (cos α2 - cos α₁) kQ L (cos α2 - cos α₁) (cos α₁ - cos α₂) (cos α₁ - cos α₂)
Transcribed Image Text:L/2 0 Ay -L/2 02 a α1 T P ΔΕ (Qdy/L) p² ΔΕ, Z 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 = =p²/y² (2).} 1. (cos α2 - cos α₁) kQ L 2. 4. kQ 3. -(cos α₁ - cos α₂) Lr 5. kQ r 6. kQ Lr kQ r (cos α2 - cos α₁) kQ L (cos α2 - cos α₁) (cos α₁ - cos α₂) (cos α₁ - cos α₂)
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