# A changing magnetic flux

1. Apr 3, 2009

### Melqarthos

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. Apr 3, 2009

### king vitamin

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.

3. Apr 3, 2009

### Melqarthos

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

4. Apr 3, 2009

### 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