Zero Induced EMF in a Changing Magnetic Flux Loop

[Melqarthos]

Homework Statement

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?

Homework Equations

Basically the most relevant equation is:

-(dɸ)/(dt)=Emf

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

 

[king vitamin]

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?

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.

 

[Melqarthos]

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

 

[Melqarthos]

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