Exam (163).pdf - Question A current I flows lengthwise in a very long thin conducting sheet of width w as shown in Figure a Assuming that the current

Exam (163).pdf - Question A current I flows lengthwise in a...

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Question:A current I flows lengthwise in a very long, thin conducting sheet ofwidth w, as shown in Figure.a) Assuming that the current flows into the paper,determine the magnetic flux density B1 at point P1(0,d).b) Use the result in part (a) to find the magnetic fluxdensity B2 at point P2(2w/3, d).Figure: A thin conducting sheet carrying a current I
Ris the distance between the source points to the field point.Find the magnetic flux density at point and in Figure 1.a)From equation (1), the magnetic flux density at the point is calculated as,
Let, and then, [The integration has been solved by taking ] [The integration has been solved by taking ] Put the value of and in to get …… (2) Thus, the required the magnetic flux density at the point is
. b)The magnetic flux density at the point is calculated asHere,denotes the magnetic flux density at due to current on left part of , anddenotes the magnetic flux density at due to current on right part of Since point is displaced by right side of origin, put in place of equation (2) to yield …… (3)Since point is situated at left side of the end point of conducting sheet, put in place of win Equation (2) to yield …… (4) . w in . .
Sum equations (3), and (4) to yield the magnetic flux density at the point ,Thus, this is the required magnetic flux density at the point .

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