Three Infinite Straight Wires 1 2 3 4 5 6 7 Three infinite straight wires are fi

Question

Three Infinite Straight Wires

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Three infinite straight wires are fixed in place and aligned parallel to the z-axis as shown. The wire at (x,y) = (-12 cm, 0) carries current I1 = 2.7 A in the negative z-direction. The wire at (x,y) = (12 cm, 0) carries current I2 = 0.7 A in the positive z-direction. The wire at (x,y) = (0, 20.8 cm) carries current I3 = 7.4 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

2)

What is By(0,0), the y-component of the magnetic field produced by these three wires at the origin?

T

3)

What is Fx(1), the x-component of the force exerted on a one meter length of the wire carrying current I1?

N

4)

What is Fy(1), the y-component of the force exerted on a one meter length of the wire carrying current I1?

N

5)

What is Fx(2), the x-component of the force exerted on a one meter length of the wire carrying current I2?

N

Explanation / Answer

a)
Bx(0,0) = u0*I3/2*pi*h

constant u=1.25663706*10^-6 mkgs-2A-2

Bx(0,0) = ((1.25663706*10^-6)*(7.4))/(2*pi*0.208)
= 7.11*10^-6 T

b)
By(0,0) = -u0/pi*d * (I1+I2)

By(0,0) = -(1.25663706*10^-6*3.4)/(pi*2*0.12)
= -5.67*10^-6 T

c)
Fx = -u0*I1/2pid (I3sin30 + I2)

=> Fx = -((1.25663706*10^-6*2.7)*(3.7+0.7))/(2*pi*2*0.12)
= -9.9*10^-6 N

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