In the figure below, a long circular pipe with outside radius R = 1.69 cm carrie

Question

In the figure below, a long circular pipe with outside radius R = 1.69 cm carries a (uniformly distributed) current i = 9.19 mA into the page. A wire runs parallel to the pipe at a distance of 3.00R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the ratio of the magnitude of the net magnetic field at point P to the magnitude of the net magnetic field at the center of the pipe is 0.899, but it has the opposite direction

Explanation / Answer

at the center

magnetic field due to circular pipe B1 = 0

magnetic field due to wire B2 = uo*I/(2*pi*3R) = -uo*I/(6*pi*R)

net field at center Bc = B1 - B2 = -uo*I/(6*pi*R)

at point P

magnetic field due to circular pipe B1 = uo*i/(2*pi*2R)

magnetic field due to wire B2 = -uo*I/(2*pi*R)

net field at point P Bp = B1 + B2 = uo*(2I-i)/(4*pi*R)

BP/Bc = -((2I-i)/I)*(3/2)

BP/Bc = -0.899

-0.899 = -((2I-0.00919)/I)*(3/2)

I = 6.56 m <<<<<<<<----------answer

direction into the page

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