PLEASE SHOW WORK, AND FORMULAS IN WRITING IF POSSIBLE, THANK YOU! 17. Two long s

Question

PLEASE SHOW WORK, AND FORMULAS IN WRITING IF POSSIBLE, THANK YOU!

17. Two long straight wires carry currents perpendicular to the xy plane. One wire carries a current of 30 A and passes through the point x = 7 cm on the x axis. The second wire carries a current of 20 A and passes through the point y = 6 cm on the y axis. (25 points) i) Determine the magnitude of the magnetic field at the origin due to the wire passing through the point on the x-axis. ii) Determine the magnitude of the magnetic field at the origin due to the wire passing through the point on the y-axis. iii) Determine the magnitude of the magnetic field at the origin due to the combined magnetic fields of the wires.

Explanation / Answer

magnetic field due to a long current carrying conductor is given by

B=mu*I/(2*pi*r)

where B=magnetic field

mu=magnetic permeability

I=current in the wire

r=perpendicular distance from the wire

direction of the magnetic field is given by the right hand thumb rule.

part a:

due to wire passing through the point x=7 cm on the x axis:

distance of the wire from origin=r=7 cm=0.07 m

current in the wire=I=30 A

then magnitude of magnetic field=B1=mu*I/(2*pi*r)

==>B1=4*pi*10^(-7)*30/(2*pi*0.07)

=>B1=8.5714*10^(-5) T

as the direction of current is not known, the direction of magnetic field can not be decided accurately.

depending upon the direction of the current, magnetic field will be either along +ve y axis or -ve y axis.

part b:

due to wire passing through the point y=6 cm on the y axis:

distance of the wire from origin=r=6 cm=0.06 m

current in the wire=I=20 A

then magnitude of magnetic field=B2=mu*I/(2*pi*r)

==>B2=4*pi*10^(-7)*20/(2*pi*0.06)

==>B2=6.6667*10^(-5) T

as the direction of current is not known, the direction of magnetic field can not be decided accurately.

depending upon the direction of the current, magnetic field will be either along +ve x axis or -ve x axis.

part c:

although the exact direction of both the magnetic fields can not be determined, one thing is sure that while direction of magnetic field due to

current on the x axis is along y axis and direction of magnetic field due to current on the y axis is along x axis.

hence both the magnetic fields are perpendicular to each other

hence net magnitude=sqrt(B1^2+B2^2)=1.0859*10^(-4) T

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