Circular loop of wire is concentric with a solenoid

In summary: N is not equal to 1. N is the number of turns of the solenoid, not the number of coils in the solenoid.Is N = 1? Because we have only a single ring? And I chose A to be the cross section of the area because that's what the equation for B is. The...
  • #1
Pochen Liu
52
2
Homework Statement
Find the loops resistance
Relevant Equations
N/A
Question:
In Figure (a), a circular loop of wire is concentric with a solenoid and lies in a plane perpendicular to the solenoid's central axis.The loop has radius 6.13 cm. The solenoid has radius 2.07 cm, consists of 8230 turns/m, and has a current i_sol varying with time t as given in Figure (b), where the vertical axis scale is set by i_s = 1.03 A and the horizontal axis scale is set by ts = 4.6 s. Figure (c) shows, as a function of time, the energy E that is transferred to thermal energy of the loop; the vertical axis scale is set by Es = 101.6 nJ. What is the loop's resistance?

I want to find B, the magnetic flux density such that I can work out what the EMF is.
From the EMF I can use
$$ P = \frac{EMF^2}{R} $$

To work out R as I know what P is since that is J/s.

However how can I find B when:
$$ B = \frac{\mu N I}{2R}$$

and I don't know what the current (I) is? As the current varies over time.If someone could provide what is going on in terms of the physics and the required next steps that would be great!
 

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  • #2
Look carefully at figures (b) and c. From (b) you can determine completely the function I(t) (that is the current as a function of time t) and from (c) you can determine completely the function E(t).
 
  • #3
Delta2 said:
Look carefully at figures (b) and c. From (b) you can determine completely the function I(t) (that is the current as a function of time t) and from (c) you can determine completely the function E(t).
Sorry I don't follow, I can find the rate of change of these with regards to time, however I don't see anything I can do it with
 
  • #4
Pochen Liu said:
Sorry I don't follow, I can find the rate of change of these with regards to time, however I don't see anything I can do it with
How can you find the rate of change of I and E w.r.t to time t?

And of course you can do many things with it, from the rate of change of current(which will be the same (up to some multiplicative constants) to rate of change of magnetic field B of the solenoid) and Faraday's law of induction you can calculate the EMF through the circular wire loop. From the rate of change of energy you can calculate the Power, due to the EMF and current, that is dissipate as heat in the resistance R of the loop.
 
  • #5
Delta2 said:
How can you find the rate of change of I and E w.r.t to time t?

And of course you can do many things with it, from the rate of change of current(which will be the same (up to some multiplicative constants) to rate of change of magnetic field B of the solenoid) and Faraday's law of induction you can calculate the EMF through the circular wire loop. From the rate of change of energy you can calculate the Power, due to the EMF and current, that is dissipate as heat in the resistance R of the loop.
To confirm, is this what you meant? I have played with the equations a little. Also, n is the density of coils/m
69839783_777321356017894_5413346727992229888_n.jpg


However I am not provided with the length of the solenoid?
 
  • #6
Your equations appear to be correct, but it all depends what A and N (the capital N in the last equation for emf) are. So please tell me what is A and what is N

And you don't need to know the length of the solenoid to answer the question. It seems to be that the solenoid is supposed to have very large length, theoretically infinite.
 
  • #7
Delta2 said:
Your equations appear to be correct, but it all depends what A and N (the capital N in the last equation for emf) are. So please tell me what is A and what is N

And you don't need to know the length of the solenoid to answer the question. It seems to be that the solenoid is supposed to have very large length, theoretically infinite.

1568115345421.png

Judging by this, A = pi * 0.0207^2 (Solenoids radius right?) And n (Not N) = 8230/m
 
  • #8
Well you are correct for A (and for n). But tell me why you chose A to be the cross section area of the solenoid and not the cross section area of the wire loop

And also tell me what is N
 
  • #9
Delta2 said:
Well you are correct for A (and for n). But tell me why you chose A to be the cross section area of the solenoid and not the cross section area of the wire loop

And also tell me what is N
Is N = 1? Because we have only a single ring? And I chose A to be the cross section of the area because that's what the equation for B is. The magnetic flux density through the solenoid as it's within the ring, but we treat the ring like a solenoid, so N = 1.
 
  • #10
Pochen Liu said:
Is N = 1? Because we have only a single ring? And I chose A to be the cross section of the area because that's what the equation for B is. The magnetic flux density through the solenoid as it's within the ring, but we treat the ring like a solenoid, so N = 1.
yes you are correct N=1. So I guess all you have to do is plug in the numbers to the equations. You also can find ##P=\frac{dE}{dt}## from figure (c), so you can solve for the resistance of the loop.
 
  • #11
Delta2 said:
yes you are correct N=1. So I guess all you have to do is plug in the numbers to the equations. You also can find ##P=\frac{dE}{dt}## from figure (c), so you can solve for the resistance of the loop.
I got 0.00054996 Ohms (Which I hope is correct??). Thank you so much!
 
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1. What is a circular loop of wire concentric with a solenoid?

A circular loop of wire concentric with a solenoid is a setup where a circular loop of wire is placed at the center of a solenoid (a coil of wire). The loop and the solenoid are aligned along the same axis and share the same center point.

2. What is the purpose of a circular loop of wire concentric with a solenoid?

The purpose of this setup is to create a magnetic field that is uniform and strong. The magnetic field produced by the solenoid is amplified by the circular loop of wire, making it more suitable for various applications such as electromagnets and generators.

3. How is the direction of the magnetic field determined in this setup?

The direction of the magnetic field is determined by the direction of the current flowing through the circular loop of wire. The right-hand rule can be used to determine the direction of the magnetic field, where the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field.

4. What factors affect the strength of the magnetic field in a circular loop of wire concentric with a solenoid?

The strength of the magnetic field in this setup is affected by the number of turns in the solenoid, the current flowing through the loop, and the radius of the loop. Increasing any of these factors will result in a stronger magnetic field.

5. What are some practical applications of a circular loop of wire concentric with a solenoid?

This setup is commonly used in electromagnets, where a magnetic field is desired to move or control objects. It is also used in generators to convert mechanical energy into electrical energy. Other applications include speakers, electric motors, and particle accelerators.

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