Consider the infinite sheet of current shown in the figures. The sheet is composed of straight, parallel wires separated by distance d and each carrying current 1. There are an infinite number of evenly-spaced wires on the sheet, and each wire is infinitely long. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point a distance D above the sheet. For the purposes of this problem, use a coordinate system such that the infinite sheet lies in the x-y plane with the current flowing in the +x-direction. The z-axis is perpendicular to the sheet, as shown. Top view y Cross-sectional view Assume that the spacing d between the wires is small compared to the distance D so that the sheet can be approximated as a uniform plane of current. Select the examples that are symmetries (or antisymmetries) of this system. antisymmetric under 180° rotations around the y-axis symmetric under translations in the x-direction symmetric under 180° rotations around the z-axis symmetric under translations in the y-direction antisymmetric under 180° rotations around the z-axis symmetric under 180° rotations around the y-axis symmetric under translations in the z-direction O O O O0
Consider the infinite sheet of current shown in the figures. The sheet is composed of straight, parallel wires separated by distance d and each carrying current 1. There are an infinite number of evenly-spaced wires on the sheet, and each wire is infinitely long. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point a distance D above the sheet. For the purposes of this problem, use a coordinate system such that the infinite sheet lies in the x-y plane with the current flowing in the +x-direction. The z-axis is perpendicular to the sheet, as shown. Top view y Cross-sectional view Assume that the spacing d between the wires is small compared to the distance D so that the sheet can be approximated as a uniform plane of current. Select the examples that are symmetries (or antisymmetries) of this system. antisymmetric under 180° rotations around the y-axis symmetric under translations in the x-direction symmetric under 180° rotations around the z-axis symmetric under translations in the y-direction antisymmetric under 180° rotations around the z-axis symmetric under 180° rotations around the y-axis symmetric under translations in the z-direction O O O O0
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Transcribed Image Text:Consider the infinite sheet of current shown in the figures. The sheet is composed of straight, parallel wires separated by distance
d and each carrying current 1. There are an infinite number of evenly-spaced wires on the sheet, and each wire is infinitely long.
Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point a distance D above the
sheet. For the purposes of this problem, use a coordinate system such that the infinite sheet lies in the x-y plane with the current
flowing in the +x-direction. The z-axis is perpendicular to the sheet, as shown.
Top view
Cross-sectional view
d
d
Assume that the spacing d between the wires is small compared to the distance D so that the sheet can be approximated as a
uniform plane of current.
Select the examples that are symmetries (or antisymmetries) of this system.
antisymmetric under 180° rotations around the y-axis
symmetric under translations in the x-direction
symmetric under 180° rotations around the z-axis
symmetric under translations in the y-direction
antisymmetric under 180° rotations around the z-axis
symmetric under 180° rotations around the y-axis
O symmetric under translations in the z-direction
2.
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