Two infinite wires have position vectors in the xy-plane r₁ = (a, b) and 72 = (-a, b) with corresponding currents i and i, respectively, let the unit vector associated with the wire element lie in the 2 direction. Analyze and solve the following problems in the xy-plane (i.e. z = 0): 1) Draw a picture representing the above scenario including the angles between the position vectors of the wires and the x-axis 2) Determine a value for the cosine and sine of the angles in part 1) in terms of the given co- ordinates 3) Determine the distance of the wires from the origin in terms of the given coordinates
Two infinite wires have position vectors in the xy-plane r₁ = (a, b) and 72 = (-a, b) with corresponding currents i and i, respectively, let the unit vector associated with the wire element lie in the 2 direction. Analyze and solve the following problems in the xy-plane (i.e. z = 0): 1) Draw a picture representing the above scenario including the angles between the position vectors of the wires and the x-axis 2) Determine a value for the cosine and sine of the angles in part 1) in terms of the given co- ordinates 3) Determine the distance of the wires from the origin in terms of the given coordinates
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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![Two infinite wires have position vectors in the xy-plane ₁ = (a, b) and ₂ = (-a, b) with corresponding
currents i and i2, respectively, let the unit vector associated with the wire element lie in the 2 direction.
Analyze and solve the following problems in the xy-plane (i.e. z = 0):
1) Draw a picture representing the above scenario including the angles between the position
vectors of the wires and the x-axis
2) Determine a value for the cosine and sine of the angles in part 1) in terms of the given co-
ordinates
Determine the distance of the wires from the origin in terms of the given coordinates
Determine the unit vectors pointing from the 2 wires to the origin (label them ₁ and 2) in terms
of the cosine and sine found in part 2
5) Determine the unit vector of the magnetic field at the origin from both wires (call them and
B₂)
6) Determine the magnetic field at the origin from both wires (call them B₁ and B₂), and draw
these vectors on the diagram from part 1)
7) Determine the total magnetic field at the origin, B
8) If i₁ = 1₂ determine appropriate values for the position vector components for the total field to
be zero at the origin.
3)
4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf1ef7c6-a145-4dbc-a50b-84dc7d2e578d%2F7d256fe6-f3e5-4089-86de-e2d9ed7cb8ef%2F39pjdxp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Two infinite wires have position vectors in the xy-plane ₁ = (a, b) and ₂ = (-a, b) with corresponding
currents i and i2, respectively, let the unit vector associated with the wire element lie in the 2 direction.
Analyze and solve the following problems in the xy-plane (i.e. z = 0):
1) Draw a picture representing the above scenario including the angles between the position
vectors of the wires and the x-axis
2) Determine a value for the cosine and sine of the angles in part 1) in terms of the given co-
ordinates
Determine the distance of the wires from the origin in terms of the given coordinates
Determine the unit vectors pointing from the 2 wires to the origin (label them ₁ and 2) in terms
of the cosine and sine found in part 2
5) Determine the unit vector of the magnetic field at the origin from both wires (call them and
B₂)
6) Determine the magnetic field at the origin from both wires (call them B₁ and B₂), and draw
these vectors on the diagram from part 1)
7) Determine the total magnetic field at the origin, B
8) If i₁ = 1₂ determine appropriate values for the position vector components for the total field to
be zero at the origin.
3)
4)
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