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Magnetic force direction

54
4
Good day All!
while trying to solve this question
coil 1.png

I use the right hand rule and according to it the Force should be directed outward (pointing toward me)
but here is the answer that puzzeld me
coil 2.png


I really don't get why it is down , and would feel very grateful if someone can explain me the reason
thanks in advance!!!
 

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Charles Link

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The way I know how to work this one is to use potential energy ## E=-\mu \cdot B ##, and use the force ## F=-\nabla E ##. The first equation comes about because torque ## \tau=\mu \times B ## with a ## \sin(\theta) ## in the cross product, and the integral of ## E=\int \tau \, d \theta ## gives the ## \cos(\theta) ## which comes in the dot product ## E=- \mu \cdot B ##. ## \\ ## In a uniform magnetic field, a magnetic dipole can experience a torque, but no net force. The force is a result of the non-uniform magnetic field. In simple terms, the equation ## E=-\mu \cdot B ## will result in an attraction of a magnetic moment that is aligned with the magnetic field to a region of stronger magnetic field, because the potential energy ## E ## at the region of stronger magnetic field is more negative. The second equation ## F=-\nabla E ## is a quantitative expression of what I have just described qualitatively. ## \\ ## Notice also, if the magnetic moment is anti-parallel with the field, the dot product will make ## \cos(180^o)=-1 ##, and the potential energy ## E ## will be more positive if you move to a region of stronger magnetic field ## B ##.
 
Last edited:
54
4
Thanks a lot!!!!
 

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