Chapter 28c - Current loops in magnetic fields Last class we found that a wire that carries a current in a magnetic field experiences a force given

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Current loops in magnetic fields Last class we found that a wire that carries a current in a magnetic field experiences a force given by, B Fi L B = × GG G i L G B F G B G This effect is put to great use in DC electric motors . To understand how these work we need to consider the forces developed on a loop of current carrying wire in a magnetic field . Since the loop of wire will rotate we need a means to maintain electrical contact between its ends and the power supply so that the current can continue to flow (without the wire getting twisted up). Current carrying wire segment
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end view V i i rotation axis The wire loop ends connect to separate copper rings on an insulated bushing. The bushing is on a roller bearing (not shown) that allows the assembly to rotate about the axis shown. Electrical contact to the power supply is via conducting brushes that electrically contact the rotating rings. This is often done as follows a b loop area = ab = A We consider this rectangular loop of side lengths a and b in a uniform magnetic field.
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i The loop carries current i , in the uniform field, initially oriented as shown. B G 3 4 1 2 B G Since BB Fi L B L B s i n = ×→ = φ GG G In this orientation, for sides 1 & 3, φ = 180 o and 0 o respectively, so, their contribution to F B is zero. axis free to rotate We determine the magnetic force on each straight segment of the loop, labeled 1 4 (for side 1 we ignore the small gap with no wire). loop area = ab x y z
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By the RHR the force on side 2 acts upwards ( ) while that on side 4 acts downwards ( ). For sides 2 & 4 , in this orientation φ = 90 o , so for them the force magnitude is, B G i 3 4 1 2 x y z axis free to rotate loop area = ab B Fi L B i a B == ˆ k + ˆ k These forces generate a torque about the axis. Recall that torque is defined, where is the moment arm from the rotation axis to the point of application of the force , with magnitude rF τ G G G r G rFsin rF r F τ= θ= = r G F G θ F F G
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bb ˆˆ ˆ iaB i ( iaB i) iabBi 22 τ=− + − =− G ( , the loop area) iAB τ = B G 3 4 1 2 axis free to rotate loop area = ab For the loop in this orientation the moment arm from the axis to wire 2 (where the magnetic force acts) is, 2 b ˆ rj
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This note was uploaded on 03/12/2010 for the course PHY PHY taught by Professor Mueller during the Spring '09 term at University of Florida.

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Chapter 28c - Current loops in magnetic fields Last class we found that a wire that carries a current in a magnetic field experiences a force given

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