In the figure below, a long circular pipe with outside radius R = 2.63 cm carrie
ID: 1600139 • Letter: I
Question
In the figure below, a long circular pipe with outside radius R = 2.63 cm carries a (uniformly distributed) current i = 14.6 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 3.80, but it has the opposite direction.
Wire O PipeExplanation / Answer
direction at centre and P are opposite.
due pipe, field at centre wil be zero.
at P, to the right.
so field due to centre will be only due to wire and that have to be to the left.
hence current in wire will be into the page.
due to wire at centre,
Bc = u0 I / (2 pi (3R)) = u0 I / ( 6 pi R) to the left
due to wire at P,
Bp1 = u0 I / (2 pi R) to the left
due to pipe,
( Bp2) (2 pi 2R) = u0 i
Bp2 = u0 i / (4 pi R) to the right
BP2 = (u0 / 2pi R) (i /2 - I )
and BP2 / Bc = 3.80
(u0 / 2pi R) (i /2 - I ) = 3.80 u0 I / ( 6 pi R)
i / 2 - I = 3.80I / 3
14.6 /2 = (3.80 / 3 + 1) I
I = 3.22 mA