Three infinite straight wires are fixed in place and aligned parallel to the z-a
ID: 2242954 • 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) = (-21 cm, 0) carries current I1 = 2.2 A in the negative z-direction. The wire at (x,y) = (21 cm, 0) carries current I2 = 1.4 A in the positive z-direction. The wire at (x,y) = (0, 36.4 cm) carries current I3 = 7.1 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?
3)What is Fx(1), the x-component of the force exerted on a one meter length of the wire carrying current I1?
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?
Explanation / Answer
uo = 4*3.14*10^-7
d = 42cm = 0.42 m
B1 = uo*I1/(2*pi*x1) -j = -2.095238095e?6 j
B2 = uo*I2*/(2*pi*x2)-j = -1.333333333e?6 j
B3 = uo*I3/(2*pi*y3) i = 3.901098901e?6 i
1) Bx = uo*I1/(2*pi*y1) = (4*3.14*10^-7*7.1)/(2*3.14*0.364)= 3.901098901e?6 T
2) By = 3.428571428e?6 T
3) Bnet at I1 = uo*I2/(2*pi*d)-j + uo*I3/(2*pi*d)*[cos30i - sin30j]
Bnet = -666.67*10^?9j + 2.927990651e?6i - 1.69047619e?6j
Bnet = 2.93*10^-6i-2.36*10^?6 j
F = I1*(LxBnet) = 2.2*(-1k x 2.93*10^-6i-2.36*10^?6 j)=-6.446*10^?6j + 5.192*10^?6 i
3) Fx = 5.192*10^?6 N
4) Fy = 6.446*10^?6 N
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