In the figure below, a long circular pipe with outside radius R = 2.14 cm carrie
ID: 1549701 • Letter: I
Question
In the figure below, a long circular pipe with outside radius R = 2.14 cm carries a (uniformly distributed) current i = 11.3 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 1.14, but it has the opposite direction.
Wire O PipeExplanation / Answer
(a)
The field at the center of the pipe (point
C) is due to the wire alone, with a
magnitude of
B_C = uo I_ wire/ 2pi ( 3R) = uo I_wire/ 6 pi R
for the wire we have
Bp_ wire > B_C
Bp = BC - BC_wire
B_P = Bp _ wire - Bp _ wire
= uo I_ wire / 2pi R - uo I/ 2pi ( 2R)
B_C = -BP
uo I_wire/ 6 pi R= - ( uo I_ wire / 2pi R - uo I/ 2pi ( 2R))
uo I_wire/ 6 pi R+ uo I_ wire / 2pi R= uo I/ 2pi ( 2R)
I_ wire ( uo / 6 pi R + 2pi R) = uo I/ 4 piR
i_ wire = 3i/8 = 3 ( 11.3 mA)/ 8 = 4.23 mA
(b)
Applying right hand rule The direction is into the page