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A changing magnetic flux 
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#1
Apr309, 02:39 PM

P: 11

1. The problem statement, all variables and given/known data
A circular wire loop of radius r= 19 cm is immersed in a uniform magnetic field B= 0.670 T with its plane normal to the direction of the field. If the field magnitude then decreases at a constant rate of −1.2×10−2 , at what rate should increase so that the induced emf within the loop is zero? 2. Relevant equations Basically the most relevant equation is: (dɸ)/(dt)=Emf 3. The attempt at a solution I'm not too sure how to attempt this problem. It would be greatly appreciated if someone could get me started. Melqarthos 


#2
Apr309, 02:47 PM

P: 172

In order for the induced EMF to be zero, (dɸ)/(dt) = 0. ɸ = B*Area if the field is perpendicular to the loop. You have dB/dt by the problem statement, so you should be able to solve for dA/dt and dr/dt using geometric relations. Also note that when you differentiate the flux, that both the area and the magnetic field are timedependent. 


#3
Apr309, 02:51 PM

P: 11

What do you mean by geometric relations? I'm not quite sure.



#4
Apr309, 03:16 PM

P: 11

A changing magnetic flux
Never mind. I got it. we just use this relationship:
(dΦ)/(dt)=(BcosΘ)(dA/dt)+(AcosΘ)(dB/dt) + AB(sinΘ)(dΘ/dt), in which case the last term is equal to zero as the angle does not change. Only the magnitude and area change. Thanks! Melqarthos 


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