Finding Charge From Changing Magnetic Flux

[SeannyBoi71]

Homework Statement

In the figure, a flexible square loop 0.700 m on a side is made of wire of resistance 0.600 Ω. A magnetic field with magnitude 1.70 T is directed onto the plane of the loop. A student crushes the wires together forming a loop of zero area in 0.350 s. Find the total amount of charge flowing through the wire.

Homework Equations

Maxwell's equations such as
∫E$\cdot$dA = Q_enclosed/epsilon nought

The Attempt at a Solution

Now I am having trouble starting this question. I am thinking that because the loop is being crushed, the area is going to be changing, which means magnetic flux is changing because $\Phi$_B=BA. And I know that magnetic flux somehow influences electric flux (forget the name of the law for this), so I'll have to use the equation listed above. Any hints please?

 

[SeannyBoi71]

Here's what I tried. I calculated Phi_B = 0.833. This next part is where I'm not sure I can actually do this. I just divided .833 by the time .35 and got dPhi/dt = 2.38, so the EMF induced is -2.38 V. Then I went V=Ed and got E= .85 Vm^-1. Then used Gauss' Law Q_enclosed = epsilon nought * E * A = 3.69 pC. This seems like an extremely small amount so I haven't entered my answer yet. Also I'm not sure if I can do half the things I did here lol.

 

[technician]

I calculated the flux through the loop.
Induced emf = change in flux per second
Current = emf/R
Current = coulombs per second... should give you the charge in coulombs (I got 1.38)

 

[SeannyBoi71]

Okay so that's right. So I was right about being able to divide B by time. But I thought current was the rate of change of charge? So why can we just use it as charge per unit time?

 

[technician]

You are correct... amps = coulombs per second.
I calculated the current from V/R ... V = induced emf, R =0.600ohms
I got the voltage to be 2.38... the same as you.
I am not certain what your V = Ed means !

 

[SeannyBoi71]

You are correct... amps = coulombs per second.
I calculated the current from V/R ... V = induced emf, R =0.600ohms
I got the voltage to be 2.38... the same as you.
I am not certain what your V = Ed means !

I was mistaken and thought I would have to use Gauss' Law because the assignment name is 'Maxwell's Equations"... so I tried solving for the electric field induced but it definitely didn't work.

 

[technician]

Are you convinced by what I did !?

 

[SeannyBoi71]

Yes I am. I did and and the answer was correct. I was just making sense of something we did.

 

[technician]

great... well done