Magnetic force and fields

1. Jun 5, 2009

Dell

http://lh6.ggpht.com/_H4Iz7SmBrbk/SikOL1lh7BI/AAAAAAAABCY/_70wWSK_-Vw/s640/DEVAN.jp [Broken]

given a square wire frame with a side of length L, placed in a constant extarnal magnetic field B, (B=B*$$\hat{k}$$). a current of i flows through the frame anticlockwise(as shown by arrows in diagram)

the frame can turn freely about the x axis (which passes through its centre)
the frame has a linear mass density of λ

a) what is the force applied on the frame?
b) what is the momentum applied of the frame?
c) what is the angular acceleration of the frame?

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a) since the force applied would be ILxB,
the force on either side parallel to the field B has no contribution since ILB*sinθ=0 (θ=0/180)
for either side perpendicular to the field ILxB=ILB

therefore my total force on the frame would be 0+0+ILB-ILB=0

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b) for the momentum i say that N=RxF=(L/2)*F=(L/2)*ILB=0.5L2IB

and since i have 2 contributors to the momentum and the are both on x-,
N=-L2IB*$$\hat{i}$$
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c) for the angular acceleration α, i need to somehow find the moment of enetria for a frame like this, and then i can say that N=Iα
α=N/I

can i use the moment of a pole 1/12(mL2) and multiply it by 2 to take into account each side??? this doesnt seem right to me, what aout the other 2 sides wgich arent revolving about their centre???

Last edited by a moderator: May 4, 2017