S13Phys2BaLec28C

# The force on one of these segments is the force on

• Notes
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The force on one of these segments is: The force on the wire as a whole is the vector sum of all differential forces on the different wire segments.

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Torque on a Current Loop Let’s say we have a rectangular loop of wire (of length b and width a) with a clockwise current immersed in a magnetic field. Use RHR on each section of the wire. For the top section, the force would point upward. X X X X X X X X X X X X X X X X X X X X B field I F top F bot F left F right What would be the direction of the magnetic force on this wire loop? For the bottom, the force would point downward. For the left, the force would point to the left. For the right, the force would point to the right.
Torque on a Current Loop The forces cancel out. So nothing will happen to the loop. But, what if the wire loop was slightly tilted ( θ ) with respect to the magnetic field. Now, we can create a torque due to these forces about a central axis. The torque on the top section will be given by: τ top = r F top sin θ τ top = a 2 F top sin θ

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Torque on a Current Loop The torque on the bottom section will be given by: The force on the top and bottom wire will have the same magnitude given by: τ bot = r F bot sin θ τ bot = a 2 F bot sin θ Also, by right hand rule, the torques will point in the same direction, such that the torque from the top and bottom add. F top = F bot = IbB sin90 ° = IbB
Torque on a Current Loop To find the total torque on the current loop, merely add the torques: τ tot = τ top + τ bot τ tot = a 2 F top sin θ + a 2 F bot sin θ τ tot = aF top sin θ = a IbB ( ) sin θ τ tot = IAB sin θ where A is the area of the loop.

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• Spring '08
• schuller
• Charge, Force, Magnetic Field, Electric charge, Ftop B

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