18 which wire will have the largest and which the

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Unformatted text preview: re loop to do mechanical work.   By running current through the loop immersed in a magnetic field we can rotate the loop. Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 21 y There is a rectangular loop (sides w, l) of current, I. What is the force on each side? What is the torque? ˆ B = B0 x 2 I z y x 3 1 4 x l w Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 22 y There is a rectangular loop (sides w, l) of current, I. What is the force on each side? The force on side 2 and 4 is 0. ˆ B = B0 x 2 I z y x 3 1 4 x l w Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 23 y There is a rectangular loop (sides w, l) of current, I. What is the force on each side? The force on side 1 and 3 will be in opposite direction and equal in magnitude. ˆ B = B0 x 2 I y x 3 1 Physics 2B - Summer Session 2 - C. Palmer z 4 x l w August 26, 2013 24 y There is a rectangular loop (sides w, l) of current, I. What is the force on each side? ˆ F1 = IlB0 ( − z ) ˆ F3 = IlB0 ( + z ) ˆ B = B0 x 2 I Physics 2B - Summer Session 2 - C. Palmer y x 3 1 Total force is 0. z 4 x l w August 26, 2013 25 z Flip the coordinate system to see the forces better. Recall torque: τ =r ×F What is the torque about the origin? y x F r1 r2 3 I I F1 ˆ F1 = IlB0 ( − z ) ˆ F3 = IlB0 ( + z ) Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 26 z What is the torque about the origin? τ = r F sin θ x y F3 θ r1 I r2 I θ F1 ˆ F1 = IlB0 ( − z ) ˆ F3 = IlB0 ( + z ) Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 27 z What is the torque about the origin? w ˆ τ 1 = IlB0 sin θ ( − y ) 2 w ˆ τ 3 = IlB0 sin θ ( − y ) 2 ˆ τ Total = IlwB0 sin θ ( − y ) x y F3 θ r1 I r2 I θ F1 ˆ F1 = IlB0 ( − z ) ˆ F3 = IlB0 ( + z ) Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 28 z ˆ τ Total = IlwB0 sin θ ( − y ) y F3 θ ˆ = I ( Area ) B0 sin θ ( − y ) r1   Same torque I r2 I   From anywhere inside θ the wire loop F1 x   For arbitrary shaped loopalways area   To keep the rotation going in the same direction one can alternate the current Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 29 ˆ τ = I ( Area ) B0 sin θ ( − y ) ˆ = ( IAn ) × B = µ × B   This motivates defining a vector with is the current times area of a loop.   The direction is given by curling the fingers of your right hand in the direction of the current.   Your thumb points in the direction of µ. Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 30 τ =µ×B U = −µ ⋅ B   The torque tends to make the magnetic dipole moment point in the direction of the magnetic field. Physics...
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