Calculating Induced EMF in a Bent Loop with Changing Magnetic Field

[GwtBc]

Homework Statement

The figure below shows a closed loop of wire that consists of a pair of equal semicircles, of radius 7.0 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic field B of magnitude 91 mT is directed perpendicular to the fold diameter and makes equal angles (of 45°) with the planes of the semicircles. The magnetic field is reduced to zero at a uniform rate during a time interval of 39 ms. During this interval, what are the (a) magnitude and (b)direction (clockwise or counterclockwise when viewed along the direction of B) of the emf induced in the loop?
https://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c30/pict_30_14.gif

Homework Equations

$\frac{\mathrm{d} \Phi }{\mathrm{d} t}= - \varepsilon, \Phi = \mathbf{B}\cdot \textbf{A}$

The Attempt at a Solution

I summed up the flux through each semicircle and divided by delta t, but that gives the wrong answer (Part A is about the magnitude so there aren't any issues with the negative sign). I asked a tutor and he thought it should be done the same way (even looked it up online and saw the same method being used) Not sure where to go from here.

 

[Biker]

Hello,

Could you attach the figure? It seems you wanted to but forgot :>

 

[GwtBc]

Can't, but I think the problem statement explains the situation clearly enough. I will add though that the field lines are coming in such that each one of them only goes through one semicircle, i.e. the flux is not 0 to begin with.

 

[cnh1995]

I summed up the flux through each semicircle and divided by delta t,

Did you take the components of B field perpendicular to the surfaces while calculating flux?

 

[GwtBc]

Did you take the components of B field perpendicular to the surfaces while calculating flux?

Yep

 

[Biker]

Your approach is correct, It is better to show your work so we can see what might have gone wrong.

 

[lychette]

Homework Statement

The figure below shows a closed loop of wire that consists of a pair of equal semicircles, of radius 7.0 cm, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic field B of magnitude 91 mT is directed perpendicular to the fold diameter and makes equal angles (of 45°) with the planes of the semicircles. The magnetic field is reduced to zero at a uniform rate during a time interval of 39 ms. During this interval, what are the (a) magnitude and (b)direction (clockwise or counterclockwise when viewed along the direction of B) of the emf induced in the loop?
https://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c30/pict_30_14.gif

Homework Equations

$\frac{\mathrm{d} \Phi }{\mathrm{d} t}= - \varepsilon, \Phi = \mathbf{B}\cdot \textbf{A}$

The Attempt at a Solution

I summed up the flux through each semicircle and divided by delta t, but that gives the wrong answer (Part A is about the magnitude so there aren't any issues with the negative sign). I asked a tutor and he thought it should be done the same way (even looked it up online and saw the same method being used) Not sure where to go from here.

what answer did you get?...I got 2.3mV

 

[GwtBc]

Your approach is correct, It is better to show your work so we can see what might have gone wrong.

Since the angle between the field and both sections of the area of the same, and the angle given is with the plane and not the normal
B*A*sin(theta) = flux
flux/change in time = emf
so:
(0.07^2*pi*91*10^-3 * sqrt(2)/2)/(39*10^-3) = 25 mV

 

[GwtBc]

what answer did you get?...I got 2.3mV

I got an answer slightly above 25 mV

 

[Biker]

I got an answer slightly above 25 mV

Yes that is the right answer, and to be precise.
25.3984 mV
Did you put your answer in an online website? or Did you find the answer to be different than what you got in a book?
If it is in an online website, Trying placing the exact value and not an approximation.