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**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 z-direction. 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.

I've attached the diagram showing what the segment looks like and I've called the point between a and b, c.

**2. Homework Equations : F=BIL**

**3. Would this be right?:**

=>

Therefore,

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

__F__ac = ILBcos90 = 0N (90° since the x-direction is orthogonal to z)__F__cb = ILBsin90 = ILB = 1.8 x 0.04 x 1.2 = 0.0864N (90° since the y-direction is orthogonal to z)=>

__F__acb =__0.0864N____F__ab = ILBsinθ = ILBsin(arctan(4/3)) = 0.8ILB = 0.8 x 1.8 x 0.05 x 1.2 =__0.0864N__Therefore,

__F__acb =__F__abOr 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