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Long, straight conductors with square cross section, each carrying current I, are laid side by side to form an infinite current sheet with current directed out of the plane of the page (Fig. P28.74). A second infinite current sheet is a distance d below the first and is parallel to it. The second sheet carries current into the plane of the page. Each sheet has n conductors per unit length. (Refer to Problem 28.73.) Calculate the magnitude and direction of the net magnetic field at (a) point P (above the upper sheet); (b) point R (midway between the two sheets); (c) point S (below the lower sheet).

Short Answer

Expert verified

(a) The magnitude and direction of the net magnetic field at (a) point P (above the upper sheet) isB=120ln

(b) The magnitude and direction of the net magnetic field at point R (midway between the two sheets) isB=120ln

(c) The magnitude and direction of the net magnetic field at point S (below the lower sheet) isBs=0

Step by step solution

01

Magnitude of infinite current sheet

Consider two infinite current sheets, where long and straight conductors with square cross-sections and each carrying current, I is laid side by side to form an infinite current sheets as shown in following figure, the current in the conductors is out of the page in the upper sheet and into the page in the lower sheet, where each sheet has n conductors per unit length. The magnetic field at a distance of a from an infinite current sheet has a magnitude of:

B=120ln

02

Magnetic field below the two sheets

At a point to the left above the sheets and points to the right below the sheet when I is out of the page. And points to the right above the sheet and points to the left below the sheet when I is into the page. Therefore, the two sheets with currents in opposite directions produce a uniform field between the sheets and zero fields out the two sheets, no matter the distance from the sheets since the field doesn鈥檛 depend on the distance from the sheet.

If the magnetic field is above the two sheets cancel that is :

BP=0

If the magnetic field between the two sheets add that is:

BR+B1+B2=120In+120InBR=0In

If the magnetic field below the two sheets cancel that is:

Bs=0

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