Calculating EMF from Magnetic Flux and Time

[jcpwn2004]

Homework Statement

A patient's breathing is monitored by wrapping a 200 turn flexible metal belt around the patient's chest. When the patient inhales, the area encircled by the coil increases by .0039m^2. The magnitude of the Earth's magnetic field is 50x10^-6 T and it makes an angle of 50 degrees with the direction perpendicular to the coil. If the patient requires 1.5s to inhale, find the average emf induced in the coil.

Homework Equations

Magnetic flux=BA. EMF= N x change in(MagFlux)/change in time.

The Attempt at a Solution

I don't understand why I'm not gettting this problem it seems pretty straight forward. I do Magnetic Flux = BA so (50x10^-6)(.0039)(cos40) which equals 1.5x10^-7. Then I use the 2nd equation and emf = 200(1.5x10^-7)/1.5 and I get 2x10^-5 V. The answer is supposed to be 16.7x10^-6 V though.

 

[mysqlpress]

I think it is the problem with "makes an angle of 50 degrees with the direction perpendicular to the coil"

and magnetic flux is defined as BA not B delta A.
The equation should be

e.m.f = -N dBA/dt = -NBdA/dt where dA is the area changed.

 

[jcpwn2004]

I think it is the problem with "makes an angle of 50 degrees with the direction perpendicular to the coil"

and magnetic flux is defined as BA not B delta A.
The equation should be

e.m.f = -N dBA/dt = -NBdA/dt where dA is the area changed.

i don't see how that makes a difference? don't you get the same thing?

 

[alphysicist]

Hi jcpwn2004

If the magnetic field is constant, the magnetic flux through a loop is

B A cos(theta)

where theta is the angle between the direction of the field and the perpendicular to the loop. So that angle in your calculation needs to be 50 degrees, not 40 degrees.

 

[mysqlpress]

perpendicular to the coil area. I would say
and
you don't actually know the magnetic flux since the area is not given, but a change in area is given.

 

[alphysicist]

Hi mysqlpress,

Would you say there is a difference between perpendicular to the coil area and perpendicular to the loop? I chose those words because that was the wording in the original problem and I don't think there is any ambiguity. But I've been wrong before.

In your first post, remember that the process of breathing will not lead to a uniform rate of change for the flux, and so we do not want to use the instantaneous emf equation with the derivative (we don't know enough to find the derivative), but the average emf equation with the differences.

I know in this problem it's rather straightforward to see that you use the difference form (all they give you is the changes) but in certain problems it could be vital to keep the definitions of each in mind. If a problem was

A single loop of wire has a magnetic flux of $\Phi = \sin(t)$ for the times from $t=0\to \pi$. What is the instantaneous induced emf magnitude in the loop during this time?

then the result would be

$${\cal E}(t)=\cos(t)$$

but if the question had been What is the average induced emf magnitude during this time? the result would be ${\cal E}=0$