In the figure below, a long circular pipe with outside radius R = 2.51 cm carrie
ID: 1599020 • Letter: I
Question
In the figure below, a long circular pipe with outside radius R = 2.51 cm carries a (uniformly distributed) current i = 11.0 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 3.19, but it has the opposite direction
Wire O PipeExplanation / Answer
at point P
magnetic field due to the circular pipe Bc = +uo*i/(2*pi*2R)
magnetic field due to the straight wire Bs = uo*I/(2*pi*R)
net magnetic field B1 = +uo*i/(2*pi*2R) + uo*I/(2*pi*R)
at center
magnetic field due to the circular pipe Bc = 0
magnetic field due to the straight wire Bs = uo*I/(2*pi*3R)
net magnetic field B2 = uo*I/(2*pi*3R)
B1/B2 = -3.19
+uo*i/(2*pi*2R) + uo*I/(2*pi*R) = -3.19* uo*I/(2*pi*3R)
i/(2) + I = -3.19*I/3
0.011/2 + I = -3.19*I/3
I = -2.66 A
(a)
magnitude I = 2.66 A
(b)
direction = INTO the page