path a T ? m path b T ? m path c T ? m path d T ? m Explain your answers. The fi

Question

path a
T ? m

path b
T ? m

path c
T ? m

path d
T ? m

Explain your answers.

The figure below shows, in cross section, several conductors that carry currents through the plane of the figure. The currents have the magnitudes I1 = 3.0 A, I2 = 4.5 A, and I3 = 2.0 A. and the directions shown. Four paths, labeled a through d, are shown. What is the line integral path a T · m path b T · m path c T · m path d T · m Explain your answers B ^ A dl for each paths? Each integral involves going around the path in the counterclockwise direction.

Explanation / Answer

according to Amperes law

int B.dl = uo times of I

where I is current

so here
-------------------------------

for path A: as net current enclosed is zero, int B. dl = 0
--------------------------------
for path B, as net current I = I1

int B.dL =uoi1 =    4*3.14 e-7 * 3

int B.dL    3.768 * 10^-6 Tm

-----------------------------

for path C:

Inet   = I1-I2 = 4.5 -3 = 1.5 A

so

int B.dL = 4*3.14 e-7 * 1.5

int Bdl = 1.88 e -6 Tm

-------------------------

for path D:

Inet = I1-(i2+i3)

Inet   = 3-(4.5 +2) = 3.5 A

so

int BdL = 4*3.14 e-7 * 3.5

int Bdl = 4.4 *10^-6 Tm

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