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) = (-19 cm, 0) carries current I1 = 3.3 A in the negative z-direction. The wire at (x,y) = (19 cm, 0) carries current I2 = 1.1 A in the positive z-direction. The wire at (x,y) = (0, 32.9 cm) carries current I3 = 7.8 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

Your submissions:

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

Explanation / Answer

Ans:-

1 ] Bx = µ0I3/2r = 4*10^-7 I3/ 2 h

Bx = 2*10^-7*7.8 /0.329 = 4.74*10^-6T   in +ve xdir

2]By =µ0 (I1 +I2 ) /2r = 4*10^-7(3.3+1.1)/2*0.19.........................................r= d/2

By = 4.63*10^-6T in –ve ydir

3]F = I L x B

Fx1 = F21 + F31 cos ........................... = cos-1(d/2/d) =60deg

       =(I1I2µ0L/2d )+(I1I3µ0Lcos/2d)

      = I1µ0L/2d (I2+I3cos)

Fx1 = 3.3*4*10^-7*1/2*0.19(3.3+7.8*cos60)

Fx1 = 2.5*10^-5 N.......in –ve x-direction

4] Fy1 =(I1I3µ0L/2d)*sin60

            = (3.3*7.8*4*10^-7*1/2*0.19)*0.866

     Fy1 = 2.35*10^-5N    -ve ydir

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