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) = (-16 cm, 0) carries current I1 = 2.2 A in the negative z-direction. The wire at (x,y) = (16 cm, 0) carries current I2 = 0.7 A in the positive z-direction. The wire at (x,y) = (0, 27.7 cm) carries current I3 = 8.4 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?

. 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

6)h14_threewiresE Another wire is now added, also aligned with the z-axis at (x,y) = (0, -27.7 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.

7) Below is some space to write notes on this problem.

A rectangular loop of wire with sides H = 31 cm and W = 75 cm carries current I2 = 0.221 A. An infinite straight wire, located a distance L = 28 cm from segment ad of the loop as shown, carries current I1 = 0.502 A in the positive y-direction.

1)What is Fad,x, the x-component of the force exerted by the infinite wire on segment ad of the loop?N

2)What is Fbc,x, the x-component of the force exerted by the infinite wire on segment bc of the loop?.N

3)What is Fnet,y, the y-component of the net force exerted by the infinite wire on the loop?N

4)Another infinite straight wire, aligned with the y-axis is now added at a distance 2L = 56 cm from segment bc of the loop as shown. A current, I3, flows in this wire. The loop now experiences a net force of zero.

What is the direction of I3?

along the positive y-direction

along the negative y-direction

5)What is the magnitude of I3?A

(Survey Question)

6)Below is some space to write notes on this problem.

Explanation / Answer

I1 = 2.2 A

I2 = 0.7 A

I3 = 8.4 A

d =

(1)

Magnetic Field due to current carrying wire is given by,

Bx = (uo*I3)/(2**r)

Bx = (4**10^-7*8.4)/(2**0.277)

Bx = 6.06 * 10^-6 T

Direction :- Towards +ve x axis.

(2)

By = (uo*I1)/(2**r) + (uo*I2)/(2**r)

By = (4**10^-7*2.2)/(2**0.16) + (4**10^-7*0.7)/(2**0.16)

By = 3.625 * 10^-6 T

Direction :- Towards -ve y axis.

(3)

Fx = (uo*I1*I2)/(2**r) + (uo*I1*I3)/(2**r) cos(60)

Fx = (4**10^-7*2.2*0.7)/(2**0.32) + (4**10^-7*2.2*8.4)/(2**0.32) * cos(60)

Fx = 6.74 * 10^-6 N

Direction :- Towards -ve x axis.

(4)

Fy = (uo*I1*I3)/(2**r) sin(60)

Fy = (4**10^-7*2.2*8.4)/(2**0.32) * sin(60)

Fy = 1.0 * 10^-5 N

Direction :- Towards -ve y axis.

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