Three infinite straight wires are fixed in place and aligned parallel to the z-a

Question

Three infinite straight wires are fixed in place and aligned parallel to the z-axis as shown. The wire at (x,y) = (-17 cm, 0) carries current I1 = 2.3 A in the negative z-direction. The wire at (x,y) = (17 cm, 0) carries current I2 = 0.8 A in the positive z-direction. The wire at (x,y) = (0, 29.4 cm) carries current I3 = 8.5 A in the positive z-direction.

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

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

6)

Another wire is now added, also aligned with the z-axis at (x,y) = (0, -29.4 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

Fy1 = F21y + F31y

F31y = -uo*I2*I1*sin60/(2*pi*d)

F31y = -(4*pi*10^-7*8.5*2.3*sin60)/(2*pi*0.34)

F31y = -9.4*10^-7 N/m

F21y = 0

Fy1 = -9.95*10^-6 N/m

++++++++++++++++++++++

Fx2 = F12x + F32x

F12x = -uo*I1*I2/(2*pi*d)

F12x = -(4*pi*10^-7*2.3*0.8)/(2*pi*0.34)

F12x = -1.1*10^-6 N/m

F32x = -(4*pi*10^-7*8.5*0.8*cos60)/(2*pi*0.34)

F32x = -2*10^-6 N/m

Fx2 = 3.1*10^-6 N/m

++++++++++++++++++++++

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.

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