I'm stuck on this problem. I think it's the 3D geometry that's giving me the biggest problem.(adsbygoogle = window.adsbygoogle || []).push({});

The current i exists in the direction shown (from left to right) in a parabolic wire segment whose equation is y = (x^2)/b in the XY plane between x = -a and x = +a. Magnetic flux density, given by B = py^2 and the B field lines are everywhere out of the paper making an angle 60 degrees to the +X axis and 60 degrees to the +Y axis.

a) Show that B can be written as [(py^2}/2)i + [(py^2}/2]j + [(py^2)/(2^(1/2))]

b) Find X, Y, and Z components of the total force on the wire.

Part a) was easy the projections in the x and y directions are just Bcos60 and z^2 = B^2 - x^2 - y^2.

Part b) is really giving me fits.

I know that dF(magnetic) = I(dl)Bsin(theta) and when B is perpendicular to dl life is great because dF = IdlB and the dFx and dFy are dFsintheta and dFcostheta respectively.

But I'm totally thrown by B not being perpendicular and having trouble with the 3-dimensionality of the problem.

Can someone please help me see.....

Thanks

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# Magnetic Force parabolic wire

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