In the figure below, a long circular pipe with outside radius R = 2.3 cm carries
ID: 1545395 • Letter: I
Question
In the figure below, a long circular pipe with outside radius R = 2.3 cm carries a (uniformly distributed) current i = 3.40 mA into the page. A wire runs parallel to the pipe at a distance of 3.00R from center to center. Find the magnitude and direction of the current in the wire such that the net magnetic field at point P has the same magnitude as the net magnetic field at the center of the pipe but is in the opposite direction.
magnitude? mA direction? ---Select--- into the page out of the page Wire O PipeExplanation / Answer
Net magnetic field at the center of the pipe is Bc = mu_o*i1/(2*pi*3R)
this Bc is due to current in wire only
i1 be the required current in the wire
magnetic field at P is Bp = Field due to wire + Field due to pipe
Bp = +mu_0*i1/(2*pi*R) - mu_o*i/(2*pi*2R)
Given that Bp = -Bc
+mu_0*i1/(2*pi*R) - mu_o*i/(2*pi*2R) = -mu_o*i1/(2*pi*3R)
mu_0/(2*pi) cancels on both sides
(i1/R)-(i/2R) = -(i1/3R)
(i1/2.3)-(3.4*10^-3/(2*2.3)) = -(i1/(3*2.3))
i1 = 0.001275 = 1.275 m A into the page