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4. Field above a spiral wire Consider a spiral of uniformly charged wire with charged per unit length 1. We'll assume that it is an Archimidean spiral where the radial coordinate is related to the angle by s = bo where b> 0 is some constant with units of length and 0 varies from = 0 to = R/b where R is the maximum of the radial coordinate. (b) (c) We will be interested in computing the 2 component of the electric field at a point r = z2 a height z above the center of the spiral. (a) Show that the line element de for this curve is given by df = bodo when >> 1. part (a). R λ 2 E₂(r) = 2лb Show that the total charge on the spiral is given by Q = AR²/(2b) in the limit from Show that the component of the electric field along 2 at r = z2 is given by λ ARGb ( 1 - VR²+Z) Hint: The integral is the same as was done in class for the charged disk. Assume the expres- sions from (a,b) hold for all o.

4. Field above a spiral wire Consider a spiral of uniformly charged wire with charged per unit length 1. We'll assume that it is an Archimidean spiral where the radial coordinate is related to the angle by s = bo where b> 0 is some constant with units of length and 0 varies from = 0 to = R/b where R is the maximum of the radial coordinate. (b) (c) We will be interested in computing the 2 component of the electric field at a point r = z2 a height z above the center of the spiral. (a) Show that the line element de for this curve is given by df = bodo when >> 1. part (a). R λ 2 E₂(r) = 2лb Show that the total charge on the spiral is given by Q = AR²/(2b) in the limit from Show that the component of the electric field along 2 at r = z2 is given by λ ARGb ( 1 - VR²+Z) Hint: The integral is the same as was done in class for the charged disk. Assume the expres- sions from (a,b) hold for all o.

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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4. Field above a spiral wire Consider a spiral of uniformly charged wire with charged per unit length 1. We'll assume that it is an Archimidean spiral where the radial coordinate is related to the angle by s = bo where b> 0 is some constant with units of length and 0 varies from p = 0 to = R/b where R is the maximum of the radial coordinate. 1 (b) part (a). (c) R We will be interested in computing the 2 component of the electric field at a point r = z2 a height z above the center of the spiral. (a) Show that the line element de for this curve is given by df = bodo when » 1. λ 2 E₂(r): = 2πb Show that the total charge on the spiral is given by Q = AR²/(2b) in the limit from Show that the component of the electric field along 2 at r= z2 is given by λ 4лεob Z √R² +2² Hint: The integral is the same as was done in class for the charged disk. Assume the expres- sions from (a,b) hold for all o.
Transcribed Image Text:4. Field above a spiral wire Consider a spiral of uniformly charged wire with charged per unit length 1. We'll assume that it is an Archimidean spiral where the radial coordinate is related to the angle by s = bo where b> 0 is some constant with units of length and 0 varies from p = 0 to = R/b where R is the maximum of the radial coordinate. 1 (b) part (a). (c) R We will be interested in computing the 2 component of the electric field at a point r = z2 a height z above the center of the spiral. (a) Show that the line element de for this curve is given by df = bodo when » 1. λ 2 E₂(r): = 2πb Show that the total charge on the spiral is given by Q = AR²/(2b) in the limit from Show that the component of the electric field along 2 at r= z2 is given by λ 4лεob Z √R² +2² Hint: The integral is the same as was done in class for the charged disk. Assume the expres- sions from (a,b) hold for all o.
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