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

Click For Summary
SUMMARY

The discussion focuses on calculating the rate of change of the magnetic field (B) required to induce a 3.4 A current in a 102-turn coil with a diameter of 3.8 cm, using copper wire with a diameter of 0.59 mm. Participants clarify the use of formulas such as R = ρL/A for resistance and B = μ₀NI/2r for magnetic field calculations. Key issues include determining the correct length (L) of the wire and the area (A) for resistance calculations. The final consensus suggests that the diameter of the coil, not the wire, should be used to find L, leading to a corrected calculation of B.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with Ohm's Law and resistance calculations
  • Knowledge of formulas for magnetic fields and coils
  • Basic proficiency in geometry for calculating areas and circumferences
NEXT STEPS
  • Study the principles of electromagnetic induction in detail
  • Learn about the application of Ohm's Law in circuit analysis
  • Explore the derivation and application of the formula B = μ₀NI/2r
  • Investigate the significance of wire diameter and coil dimensions in electrical calculations
USEFUL FOR

Students in physics or electrical engineering, educators teaching electromagnetic theory, and anyone involved in practical applications of electromagnetism and circuit design.

BuBbLeS01
Messages
602
Reaction score
0

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?
 
Physics news on Phys.org
Is there an answer to compare to at the back of the book?
 
no because its an even number :(
 
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.
 
is r the radius of the coil or th wire??
 
well i did the radius of the coil and its wrong but thanks for trying
 
How do you know its wrong?
 
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.
 
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!
 
  • #10
Yes you do have L because you know the diameter of the coil and how many turns there are.
 
  • #11
Isn't the L for B=UIN/L the length of the solenoid not the length of the wire?
 
  • #12
oh yea...ugh I hate this problem!
 
  • #13
silvashadow said:
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.
 
  • #14
hage567 said:
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?
 
  • #15
How do I find L with having the diameter and number of turns??
 
  • #16
I was going to find E using I = E/R then use that in the equation...
E = A * B/t to get the rate
 
  • #17
BuBbLeS01 said:
How do I find L with having the diameter and number of turns??

Well, circumference=pi*diameter, lol 102 turns = 102 circumferences
 
  • #18
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??
 
  • #19
BuBbLeS01 said:
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.
 
  • #20
BuBbLeS01 said:
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.
 
  • #21
BuBbLeS01 said:
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.
 
  • #22
silvashadow said:
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.
 
  • #23
and the length would be the length of the wire not the coil right
 
  • #24
Yes, that's right.
 
  • #25
hage567 said:
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.
 
  • #26
then in the equation E = A * B/t do I use the area of the coil?
 
  • #27
oh noooo I got it wrong! My final answer was 53.6469 T/s
 
  • #28
any other ideas?
 
  • #29
BuBbLeS01 said:
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.
 
  • #30
hage567 said:
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
 

Similar threads

Induced current and force on circular loop in varying magnetic field
  • · Replies 4 ·
Replies
4
Views
1K
Forces acting on a coil due to a varying magnetic field
  • · Replies 12 ·
Replies
12
Views
3K
Induced Current Direction in a Changing Magnetic Field
  • · Replies 1 ·
Replies
1
Views
2K
How Does Induced Current Change with Loop Acceleration Through a Magnetic Field?
  • · Replies 8 ·
Replies
8
Views
2K
Induced current of a coil on another coil
  • · Replies 6 ·
Replies
6
Views
4K
How Does Induced Current Vary in a Metal Coil Within a Magnetic Field?
  • · Replies 16 ·
Replies
16
Views
2K
Induced Current in a Coil with Changing Magnetic Field
  • · Replies 5 ·
Replies
5
Views
11K
Electromagnetic effects and Magnetic Fields Questions
  • · Replies 2 ·
Replies
2
Views
2K
Solving Magnetic Field & Current Direction Problems
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Induced Current in a Coil Surrounding a Changing Current Solenoid
  • · Replies 5 ·
Replies
5
Views
4K