52••• A thin conducting sheet in the z = 0 plane carries current in the – x dire

Question

52••• A thin conducting sheet in thez = 0 plane carries current in the –xdirection (Figure 27-58a).The sheet extends indefinitely in all directions and the current isuniformly distributed throughout the sheet. To find the directionof the magnetic field at point P consider the field dueonly to the currents I1 andI2 in the two narrow strips shown. Thestrips are identical, so I1 =I2. (a) What is the direction of themagnetic field at point P due to justI1 and I2? Explainyour answer using a sketch. (b) What is the direction ofthe magnetic field at point P due to the entiresheet? Explain your answer. (c) What is the direction ofthe field at a point to the right of point P (wherey 0)? Explain your answer. (d) What isthe direction of the field at a point below the sheet (wherez < 0)? Explain your answer using a sketch.(e) Apply Ampère’s law to the rectangularcurve (Figure 27-58b)to show that the magnetic field strength at point P isgiven by B = 0, where = dI/dy is the current per unit length along they axis.

Explanation / Answer

(a) The magnetic field, I believe, points to the right since thevertical components do cancel . k is going into the paper, i isgoing to the right... so the magnetic field, B, points to -idirection. Difficult to sketch on a computer so I hope thishelps! (b) HAHAHA this is so like Tipler and Mosca. By their ownadmission, the sheet is infinite! The case holds the same as in (a)in this case, so B at P is in the -i direction! (c) I believe below the sheet B should point to the LEFT, or in idirection... but this one I am not sure on. Check this against thebook. (d) I do not have the figure in front of me, so it is a little moredifficult to do this one. From my notes before the turnover from2004-2009, we were required to prove on a figure that B = (1/2)0i. So, going off that maybe this is of some assistance We had an enclosed current w. The contour integral was then2wB. So B = (-0/2)i at any point above the sheet. Man these were some difficult problems.

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