What is the induced current in a loop due to a time-varying magnetic field?

[BroIIy]

Hello, this is my 1st time asking a question. May I have some assistance?
I will just copy and paste the question so that I don't mess up anything

Homework Statement

A single-turn circular loop of radius 0.08 m and resistance 6 is coaxial with a solenoid of length 90 cm and a radius of 0.04 m, with 1950 turns. A variable resistor, as indicated in Fig. 30-37, is varied in such a way that the solenoid current falls linearly from 5 A to 1.4 A in 0.3 sec.

link==> http://www.photodump.com/BroIIy/30-37fig.html <==
Figure 30-37

(a) What is the induced current in the loop?

Homework Equations

not really sure, if I did know I could solve it.

The Attempt at a Solution

R1 = .08
Resistance = 6
L = .9
R2 = .04
N = 1950
I1 = 5
I2 = 1.4
T = .3
u_o = 4*pi*10^-7

I3 = E / Resistance
E = (Bf - Bo) * A / T (Bf = Magnetic field final, && Bo = Magnetic field initial)

this is where it gets confusing for me
Bf = u_o * N * I2 / L ?
Bo = ?
A = pi * R1^2 ?

is any of this even in the right direction?
Thank you for your time.

 

[Doc Al]

I3 = E / Resistance
E = (Bf - Bo) * A / T (Bf = Magnetic field final, && Bo = Magnetic field initial)

Good. You are applying Faraday's law.

this is where it gets confusing for me
Bf = u_o * N * I2 / L ?

Good. This is the magnetic field inside the solenoid.

Bo = ?

Just use I1.

A = pi * R1^2 ?

Looks good.

is any of this even in the right direction?

You're doing fine.

 

[BroIIy]

1st off, thank you Doc Al for taking the time to try and help me however
i don't understand, using my variables is this what you mean? or is there something I am missing?

I3 = E / Resistance
E = (Bf - Bo) * A / T (Bf = Magnetic field final, && Bo = Magnetic field initial)
Bf = .0038117991
Bo = 5 ??
A = .020106193
E = ( ( .0038117991 ) - ( 5 ) ) * ( .020106193 ) / .9
E = - .1116159158
I3 = ( - .1116159158 ) / 6
I3 = -.0186026526 ??

or did you mean
Bo = u_o * N * I1 / L ??
Bo = .0136135682
E = ( ( .0038117991 ) - ( .0136135682 ) ) * ( .020106193 ) / .9
E = -2.18973623E-4
I3 = ( -2.18973623E-4 ) / 6
I3 = ( -3.64956038E-5 )

i must warn you i really don't have a full understanding of these concepts. in the book we are using the whole section on this field is only a paragraph long (i can type it out for you if you like). now i have researched (to the best of my abilities) using the internet and also have looked up this information in the other physics books i have stacked around me and this ^ is as far as i was able to get. I am almost 100% sure that the missing concept is from a previous chapter, however we are covering a chapter a day and I am not really absorbing the information all that well. especially when the concepts stack on each other and I am still struggling with the basics.

here is an example of how confused i am about this section, i went into class knowing from a lifetime of experience that same sign magnets repel and opposites attract, then the teacher tried explaining that exact same concept and ended up confusing me. i then started getting all the questions wrong and constantly kept asking the teacher to explain to me why i kept getting them wrong and he kept answering in the same confusing way. it took me a day to figure out that my initial thoughts (same sides repel opposites attract) was the correct format (it took me a day because i wasnt able to get home, and tbh even while typing that I am still confused about it... and it is very annoying...) so what i need here is a big kick in the right direction.

this chapter will be due by the end of the night, and we will be moving on to Magnetism and Matter (due by tomorrow night) but without understanding how the basics work i will only do worse and worse as these chapters continue. (the last chapter i missed 1 question and had absolutly no idea how to get the right answer, and this chapter I am down to 2 questions remaining, this one i atleast got this far while the 2nd question i don't even know where to begin...but next chapter will i miss 3?)

i have been working on these 2 questions for the past 9 hours, so I am going to go to bed now. if anyone feels like taking me by the hand and walking me through this please do so, otherwise when i wake up hopefully my renewed mind will click a bit better. have a good day everyone and good night =)

 

[Doc Al]

1st off, thank you Doc Al for taking the time to try and help me however
i don't understand, using my variables is this what you mean? or is there something I am missing?

I3 = E / Resistance
E = (Bf - Bo) * A / T (Bf = Magnetic field final, && Bo = Magnetic field initial)
Bf = .0038117991
Bo = 5 ??
A = .020106193
E = ( ( .0038117991 ) - ( 5 ) ) * ( .020106193 ) / .9
E = - .1116159158
I3 = ( - .1116159158 ) / 6
I3 = -.0186026526 ??

No, I meant for you to calculate Bo just like you calculated Bf. Using I1 instead of I2, of course.

or did you mean
Bo = u_o * N * I1 / L ??
Bo = .0136135682
E = ( ( .0038117991 ) - ( .0136135682 ) ) * ( .020106193 ) / .9
E = -2.18973623E-4
I3 = ( -2.18973623E-4 ) / 6
I3 = ( -3.64956038E-5 )

Yes, that's what I mean. (I didn't check your full arithmetic, but the method looks OK.)

 

[BroIIy]

thank you Doc Al i found out what i had been doing wrong, i had the entering the wrong numbers and had the wrong Area. here is the solution

R1 = .08
Resistance = 6
L = .9
R2 = .04
N = 1950
I1 = 5
I2 = 1.4
T = .3
u_o = 4*pi*10^-7

I3 = E / Resistance
E = (Bf - Bo) * A / T

Bf = u_o * N * i2 / L
Bo = u_o * N * i1 / L
A = pi * R2^2 <--R2 not R1
E = (Bf - Bo) * A / T
i3 = E / Resistance = Answer (note: its positive)