A copper water pipe has an inner radius a = 1.384cm and an radius diameter b = 1

Question

A copper water pipe has an inner radius a = 1.384cm and an radius diameter b = 1.588cm. If the pipe is long compared to its radius, it can be modeled as an infinite cylindrical conductor. Let a current I flow down the pipe such that the current is uniformly distributed through the copper. The current flows into the page. An end view of the system is drawn below. Draw the magnetic field in all regions. Calculate the magnetic field symbolically in all regions. Suppose the pipe carries a current I = 10A. What is the magnetic field at a point P at 1.486cmx as drawn below? Let the origin be along the axis of the pipe. Report the field as a vector.

Explanation / Answer

(b). this figure shows a toroid here a current I flowing in this toroid

According to the low of ampere

integration of[dot product of magnetic flux intencity with lenth]=U0 X sum of current

integration[B.dI.cosQ] = U0 sum of I

at the second condition we get

cosQ = 1 & sum of dL = 2 X3.14 r

so B = U0 N I / (2 pie r)

at first & third position wer get

sum f I = 0

so magnetic field's intencity B = 0

(c) I = 10 amp & R = 1.486 x^

so by given formula

B=4 X3.14X10-9X10 / (2X3.14X 1.486X10-2)

B=1.3458X10-6   X^   T

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