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
At what rate should what increase? The radius? or just the area of the wire? 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 time-dependent.
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