P29_043

# P29_043 - 43. Consider an inﬁnitesimal segment of the...

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Unformatted text preview: 43. Consider an inﬁnitesimal segment of the loop, of length ds. The magnetic ﬁeld is perpendicular to the segment, so the magnetic force on it is has magnitude dF = iB ds. The horizontal component of the force has magnitude dFh = (iB cos θ) ds and points inward toward the center of the loop. The vertical component has magnitude dFv = (iB sin θ) ds and points upward. Now, we sum the forces on all the segments of the loop. The horizontal component of the total force vanishes, since each segment of wire can be paired with another, diametrically opposite, segment. The horizontal components of these forces are both toward the center of the loop and thus in opposite directions. The vertical component of the total force is Fv = iB sin θ ds = (iB sin θ)2πa . We note the i, B , and θ have the same value for every segment and so can be factored from the integral. ...
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## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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