How Fast Must the Magnetic Field Change to Induce a 3.4 A Current in a Coil?

[BuBbLeS01]

Homework Statement

A 102-turn, 3.8-cm-diameter coil is made of 0.59-mm diameter copper wire. A magnetic field is perpendicular to the coil. At what rate must B increase to induce a 3.4 A current in the coil? The resistivity of copper is 1.7·10-8 Ω·m.

Homework Equations

The Attempt at a Solution

A = (0.00059/2)^2 * pi = 2.734 x 10^-7
I = 3.4 A
I don't what to do?

 

[silvashadow]

Is there an answer to compare to at the back of the book?

 

[BuBbLeS01]

no because its an even number :(

 

[silvashadow]

B=µoNI/2r, B is magnetic force, µo is magnetic constant, N is number of turns, I is current, r is radius

I think that's it but that R is unused in the problem, and it concerns me that I missed something.

 

[BuBbLeS01]

is r the radius of the coil or th wire??

 

[BuBbLeS01]

well i did the radius of the coil and its wrong but thanks for trying

 

[silvashadow]

How do you know its wrong?

 

[BuBbLeS01]

its my homework problem and our homework is on lon-capa...so we have like 4 tries for each problem and tells you when you enter the answer.

 

[BuBbLeS01]

oh my gosh this problem is driving me nuts I can't figure it out! I tried using all sorts of formulas like...
R = pL/A to get the resistance but I don't have L
So then I tried...
B = U*I*(N/L) to get L but I don't have B!

 

[hage567]

Yes you do have L because you know the diameter of the coil and how many turns there are.

 

[silvashadow]

Isn't the L for B=UIN/L the length of the solenoid not the length of the wire?

 

[BuBbLeS01]

oh yea...ugh I hate this problem!

 

[hage567]

Isn't the L for B=UIN/L the length of the solenoid not the length of the wire?

I was referring to the L in the resistivity equation that Bubbles was asking about.

 

[silvashadow]

I was referring to the L in the resistivity equation that Bubbles was asking about.

Oh I see. What's the step after finding R?

 

[BuBbLeS01]

How do I find L with having the diameter and number of turns??

 

[BuBbLeS01]

I was going to find E using I = E/R then use that in the equation...
E = A * B/t to get the rate

 

[silvashadow]

How do I find L with having the diameter and number of turns??

Well, circumference=pi*diameter, lol 102 turns = 102 circumferences

 

[BuBbLeS01]

oh lol...ok so my length is 9.8696 the when I use R = pL/A is it the area of the wire or coil??

 

[hage567]

I was going to find E using I = E/R then use that in the equation...
E = A * B/t to get the rate

This is what I would try.

 

[hage567]

oh lol...ok so my length is 9.8696 the when I use R = pL/A is it the area of the wire or coil??

The wire, since that is what you are finding the resistance of.

 

[silvashadow]

oh lol...ok so my length is 9.8696 the when I use R = pL/A is it the area of the wire or coil??

Area of wire, cross section area.

 

[hage567]

Isn't the L for B=UIN/L the length of the solenoid not the length of the wire?

The question did not actually state that this was a solenoid. It said it was a loop of 102 turns with a magnetic field perpendicular to it (so going through it). The magnetic field is not being produced by the coil. So I don't think the B = U*I*(N/L) equation is what you are looking for here, IMO.

 

[BuBbLeS01]

and the length would be the length of the wire not the coil right

 

[hage567]

Yes, that's right.

 

[silvashadow]

The question did not actually state that this was a solenoid. It said it was a loop of 102 turns with a magnetic field perpendicular to it (so going through it). The magnetic field is not being produced by the coil. So I don't think the B = U*I*(N/L) equation is what you are looking for here, IMO.

Oh I see. Thanks for setting me straight. I'm still learning and your opinion is very helpful to me.

 

[BuBbLeS01]

then in the equation E = A * B/t do I use the area of the coil?

 

[BuBbLeS01]

oh noooo I got it wrong! My final answer was 53.6469 T/s

 

[BuBbLeS01]

any other ideas?

 

[hage567]

oh noooo I got it wrong! My final answer was 53.6469 T/s

I get a different answer than this. Try checking your math over carefully and see what you get.

 

[BuBbLeS01]

I get a different answer than this. Try checking your math over carefully and see what you get.

I did it twice but I am still getting the same answer let me show you what I did maybe I missed something...
I have...
I = 3.4 A
p = 1.7 e^-8
Dcoil = 0.0308 m
Dwire = 0.00059 m
Acoil = 7.4506 e^-4
Awire = 2.73397e6-7

C = pi*Dwire...

So L = pi*Dwire*102 = 0.18906m

R = p*Lwire/Awire = 0.0117559 Ohms

I = E/R...E = IR = 0.03997 V

E = Acoil * (B/t)...B/t = E/Acoil = 53.6469 T/s

 

[hage567]

Acoil = 7.4506 e^-4

I don't get this. I think you may have made a calculator error. The diameter is 0.038 m, right?

So L = pi*Dwire*102 = 0.18906m

This should be Dcoil instead of Dwire. Dwire tells you nothing of how long the wire is. The diameter of the coil tells you that.

If you fix these two things I think the rest should be OK.

 

[BuBbLeS01]

okay so I got an answer or 35.243 T/s and it's still wrong :(

 

[BuBbLeS01]

actually I forgot to change the L value when I calculated the Resistance so now I am getting 2269.9 T/s which seems extremely large! Is that what you got?