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