Two very long parallel wires are separated by a distance d = 8.4 cm and each car

Question

Two very long parallel wires are separated by a distance  d= 8.4 cm and each carry a current  I = 16.8 A currents in the z-direction.

Part A:

Find the vector magnetic field due to the two wires at the point P which is positioned a distance L= 13.2cm from one wire and a distance w=  12.1 cm from the other. See figure(Figure 1) . Express the field direction as an angle relative to the positive x-axis.

[Hint: The relevant angles may be found using the Law of Cosines ]

|B| = _______________T

= ___________   relative to the positive x-axis

Explanation / Answer

First we have to find coordinates of point P.

L sin@ + w sin@ = d

sin@ = 8.4 / (13.2 + 12.1) = 19.39 degrees

so angle of L to the x-axiz = 2@ =38.78 deg

Magnetic field due to current carrying wire = u0*I / 2pi R

for wire at origin :

B1 = 4pi x 10^-7 x 16.8 / (2 xpi x 0.132 ) = 2.54 x10^-5 T

Direction = 90 + 38.78 =128.78 deg

vector B = 2.54 x 10^-5 ( cos128.78i + sin128.78j ) T

due to Wire at y-axis :

B2 = 4pi x 10^-7 x 16.8 / (2 x pi x 0.121) =2.78 x 10^-5 T

Direction = 90 - 19.39 = 70.61 deg

vector B2 = 2.78 x 10^-5 ( cos70.61i + sin70.61 j) T

so magnetic field at P :

B = B1 + B2 = (- 0.668 i + 4.60 j) x 10^-5 T

magnitude |B| = sqrt(0.668^2 + 4.60^2) x10^-5 =4.65 x 10^-5 T

direction = 180 - tan^-1( 4.60 / 0.668) =98.26 deg

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