Infinitely many long, straight conductors with square cross sections are laid side-by-side to form an infinitely large sheet of current. Each conductor carries a current I that is distributed uniformly over the cross section of the conductor. The conductors lie in the xy-plane, are parallel to the y-axis, and carry current in the +y-direction. There are n conductors per unit length measured along the x-axis. ● ● I X y z (a) The magnetic field above the current sheet points in the -x-direction, and the field below the sheet points in the +x-direction. Argue why this must be true based on the symmetry of the current distribution. (b) Use Ampere's law to find the magnitude of the magnetic field a distance a above the current sheet. (Hint: Your Amperian loop should be rectangular and enclose some current. At a given point on the Amperian loop, the magnetic field should be either parallel or perpendicular to the integration path.)

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6. Infinitely many long, straight conductors with square cross sections are laid side-by-side to form an
infinitely large sheet of current. Each conductor carries a current I that is distributed uniformly over
the cross section of the conductor. The conductors lie in the xy-plane, are parallel to the y-axis, and
carry current in the +y-direction. There are n conductors per unit length measured along the x-axis.
y
9000 c
Z
I
X
(a) The magnetic field above the current sheet points in the -x-direction, and the field below the
sheet points in the +x-direction. Argue why this must be true based on the symmetry of the
current distribution.
(b) Use Ampere's law to find the magnitude of the magnetic field a distance a above the current
sheet. (Hint: Your Amperian loop should be rectangular and enclose some current. At a given
point on the Amperian loop, the magnetic field should be either parallel or perpendicular to the
integration path.)
Transcribed Image Text:6. Infinitely many long, straight conductors with square cross sections are laid side-by-side to form an infinitely large sheet of current. Each conductor carries a current I that is distributed uniformly over the cross section of the conductor. The conductors lie in the xy-plane, are parallel to the y-axis, and carry current in the +y-direction. There are n conductors per unit length measured along the x-axis. y 9000 c Z I X (a) The magnetic field above the current sheet points in the -x-direction, and the field below the sheet points in the +x-direction. Argue why this must be true based on the symmetry of the current distribution. (b) Use Ampere's law to find the magnitude of the magnetic field a distance a above the current sheet. (Hint: Your Amperian loop should be rectangular and enclose some current. At a given point on the Amperian loop, the magnetic field should be either parallel or perpendicular to the integration path.)
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