Three infinite straight wires are fixed in place and aligned parallel to the z-a
ID: 1453661 • Letter: T
Question
Three infinite straight wires are fixed in place and aligned parallel to the z-axis as shown. The wire at (x,y) = (-20 cm, 0) carries current I1 = 2.6 A in the negative z-direction. The wire at (x,y) = (20 cm, 0) carries current I2 = 0.9 A in the positive z-direction. The wire at (x,y) = (0, 34.6 cm) carries current I3 = 8.6 A in the positive z-direction.
1)
What is Bx(0,0), the x-component of the magnetic field produced by these three wires at the origin?T
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2)
What is By(0,0), the y-component of the magnetic field produced by these three wires at the origin?T
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3)
What is Fx(1), the x-component of the force exerted on a one meter length of the wire carrying current I1?N
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4)
What is Fy(1), the y-component of the force exerted on a one meter length of the wire carrying current I1?N
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5)
What is Fx(2), the x-component of the force exerted on a one meter length of the wire carrying current I2?N
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6)
Another wire is now added, also aligned with the z-axis at (x,y) = (0, -34.6 cm) as shown. This wire carries current I4 A. Which of the following statements is true?
If I4 is directed along the positive z-axis, then it is possible to make the y-component of the magnetic field equal to zero at the origin.
If I4 is directed along the negative z-axis, then it is possible to make the y-component of the magnetic field equal to zero at the origin.
If I4 is directed along the positive z-axis, then it is possible to make the x-component of the magnetic field equal to zero at the origin.
If I4 is directed along the negative z-axis, then it is possible to make the x-component of the magnetic field equal to zero at the origin.
Explanation / Answer
only 4 parts at a time please:
1)
B1 will be directed along -y axis
B1 = miuo*I1/(2*pi*d1) (-y)
=(1.2566*10^-6 * 2.6) / (2*pi*0.2) (-y)
= -2.6*10^-6 y T
B2 will be directed along -y axis
B1 = miuo*I2/(2*pi*d2) (-y)
=(1.2566*10^-6 * 0.9) / (2*pi*0.2) (-y)
= -9.0*10^-7 y T
B2 will be directed along x axis
B1 = miuo*I3/(2*pi*d3) (x)
=(1.2566*10^-6 * 8.6) / (2*pi*0.346) (x)
= 4.97*10^-6 x T
Bx(0,0) = 4.97*10^-6 T
2)
By(0,0) = -2.6*10^-6 -9.0*10^-7
= -3.5*10^-6 T
3)
|Fx| = BY*I1*L
= 3.5*10^-6 * 2.6* 1
= 9.1*10^-6 N
it is directed along negative x axis
Answer: - 9.1*10^-6 N
4)
|Fy| = Bx*I1*L
= 4.97*10^-6 * 2.6* 1
= 1.29*10^-5 N
it is directed along negative y axis
Answer: - 1.29*10^-5 N
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