• BuBbLeS01
In summary, a 102-turn, 3.8-cm-diameter coil made of 0.59-mm diameter copper wire is placed in a magnetic field perpendicular to the coil. The goal is to find the rate at which the magnetic field must increase to induce a 3.4 A current in the coil. Using the formula B=µoNI/2r, where B is magnetic force, µo is the magnetic constant, N is the number of turns, I is the current, and r is the radius, and taking into account the resistivity of copper (1.7·10-8 Ω·m), it is found that the length of the wire is 0.18906m and the resistance
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.

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?

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!

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

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

oh yea...ugh I hate this problem!

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.

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?

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

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

BuBbLeS01 said:
How do I find L with having the diameter and number of turns??

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

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??

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.

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.

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.

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.

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

Yes, that's right.

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.

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

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

any other ideas?

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.

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

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.

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

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?

1. What is the process for finding the rate of magnetic field?

The process for finding the rate of magnetic field involves using a magnetometer to measure the strength and direction of the magnetic field at different points in space and time. This data is then used to calculate the rate of change of the magnetic field over time.

2. What is the unit of measurement for the rate of magnetic field?

The unit of measurement for the rate of magnetic field is tesla per second (T/s) or, more commonly, nanotesla per second (nT/s). This unit represents the change in magnetic field strength over time.

3. Can the rate of magnetic field change over time?

Yes, the rate of magnetic field can change over time. This can be due to various factors such as the movement of charged particles in the Earth's magnetic field or the presence of other magnetic fields in the environment.

4. How is the rate of magnetic field used in scientific research?

The rate of magnetic field is used in various scientific research fields, including geophysics, astrophysics, and materials science. It can provide insights into the behavior of magnetic fields in different environments and help researchers understand the underlying physical processes.

5. Are there any limitations to measuring the rate of magnetic field?

There are some limitations to measuring the rate of magnetic field, such as the precision of the magnetometer used and the presence of external sources of magnetic interference. Additionally, the rate of magnetic field can only be measured at specific points in space and time, so it may not capture the full picture of the magnetic field's behavior.

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