In the figure, if a = 2.0 cm, b = 4.0 cm, and I = 2.0 A, what is the magnitude o

Question

In the figure, if a = 2.0 cm, b = 4.0 cm, and I = 2.0 A, what is the magnitude of the magnetic field at point P?(picture below)

Not I know the currents are moving in opposite directions so they subtract from each other. And I have to use the equation B=uI/2pi*d. My problem is in determining how to calculate (d). Ive looked up a solution for this problem and dont understand why B=uI/8(1/a + 3/b). I put a side note in bold about the problem area.

Heres his solution:

B = ? I / 2r

Bb = (? I / 2b)* (3/4) which is the B field from full loop divided by 4 so it occupies 3/4 <--This right here, I dont understand why its divided by 4,can someone give me a explanation as to how to use this rule?

Ba = (? I / 2a)* (1/4)

since they are all clockwise

B = ? I / 8a + ? I 3 / 8 b =

= ( ? I /8) ( 1/a + 3/b ) =

= (4pi x 10-7 * 2 / 8 ) ( 1 / 0.02 + 3 / 0.04 ) =

= 39*10-6 T

Explanation / Answer

It's very simple.Forget the complex loop for some time(we will come to it from basics like how it is made)

You've to break and derive the loop in two parts and then see it's mathematics.

part 1;ASSUME THAT YOU'VE A COMPLETE CIRCULAR LOOP(HOLLOW) OF RADIUS "b".I tell you to cut it in 4 equal parts.SO YOU'LL CUT IT ALONG PERPENDICULARS FROM CENTRE P(along dotted lines).

NOW we take a CIRCULAR smaller loop(HOLLOW) of radius 'a' and again divide it in 4 equal parts(same way)

SO YOU'VE 8 parts in all (4 with radius "a" and 4 with rad. "b")

part2; SELECT 3 PARTS HAVING RADIUS "a" and one part with radius 'b' and join them as in the figure you've posted....

MATHEMATICALLY; PART1=circle (of radius)A IS DIVIDED BY 4 AND IT'S 3 PARTS ARE TAKEN IN CONSIDERATION=(a/4)*3....like 3/4 parts of cake just considering its circumference

SIMILARLY CIRCLE B IS DIVIDED BY 4 AND ITS 1 PART IS TAKEN INTO CONSIDERATION=(b/4)*1

THUS B=(u*I)/C......(C=CIRCUMFERENCE=2*PIE*r)...what we actually divided was circumference

adding their field independantly(considering directions you get the required solution)....;)

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