1. "A wire segment carries a current of 1.8A from a to b. There is a uniform magnetic field of 1.2T acting in the zdirection. Find the total force on the wire and show that the total force is the same as if the wire were a straight segment from a to b".
I've attached the diagram showing what the segment looks like and I've called the point between a and b, c.
2. Relevant equations: F=BIL
3. Would this be right?:
Fac = ILBcos90 = 0N (90° since the xdirection is orthogonal to z)
Fcb = ILBsin90 = ILB = 1.8 x 0.04 x 1.2 = 0.0864N (90° since the ydirection is orthogonal to z)
=> Facb = 0.0864N
Fab = ILBsinθ = ILBsin(arctan(4/3)) = 0.8ILB = 0.8 x 1.8 x 0.05 x 1.2 = 0.0864N
Therefore, Facb = Fab
Or is it just a coincidence that the two values come out to be the same? Because I don't really understand why it would be cos90 from a to c and sin90 from c to b =s
I've attached the diagram showing what the segment looks like and I've called the point between a and b, c.
2. Relevant equations: F=BIL
3. Would this be right?:
Fac = ILBcos90 = 0N (90° since the xdirection is orthogonal to z)
Fcb = ILBsin90 = ILB = 1.8 x 0.04 x 1.2 = 0.0864N (90° since the ydirection is orthogonal to z)
=> Facb = 0.0864N
Fab = ILBsinθ = ILBsin(arctan(4/3)) = 0.8ILB = 0.8 x 1.8 x 0.05 x 1.2 = 0.0864N
Therefore, Facb = Fab
Or is it just a coincidence that the two values come out to be the same? Because I don't really understand why it would be cos90 from a to c and sin90 from c to b =s
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