# Calculating EMF in Metal Detector Coils

• Sir_Pogo
In summary, the conversation discusses a problem involving a loop configuration for constructing a metal detector. The problem involves two concentric circular coils of wire with different radii and turns. The current in the larger coil has a time dependence and the goal is to find the magnitude of the EMF induced in the smaller coil at a specific time. The conversation includes attempts at solving the problem using Faraday's Law and equations related to velocity and force. The suggestion is made that the answer may require a negative sign.
Sir_Pogo
Can i get some help with this problem?
This problem deals with the basic loop configuration you will use in the laboratory to construct a metal detector. Two concentric circular coils of wire lie in a plane. The larger coil has 49 turns and a radius of a = 7.90 cm. The smaller coil also has 49 turns but has a radius of b = 0.85 cm. The current in the larger coil has a time dependence given by = Io sin(ωt) where ω = 14,000 rad/s and Io = 0.50 A. What is the magnitude of the EMF induced in the small coil at t = 2.00 s if you make the approximation that the magnetic field inside the small coil is spatially uniform?

Show us some attempt to solve the problem. What do you know that you think is relevant to the solution?

Are there any hints on this one...I am using Faraday's Law
where EMF = N*(change in flux over change in time). The
magnetic flux is equal to BA, which is the B for the center
of a loop (with radius of the outer circle) times A for the
inner circle...my final equation is coming out something
like this...[(N^2)*Pi*Rb^2*mu*I(nought)*w*cos(w*t)]/(2*Ra)

This is long, but it seems right to me...Any suggestions?

the velocity induces an emf, the emf gives a current, and
the current gives a backward force F=ILB, so you can set up
and equation mdv/dt=F=-Cv, for some const C you will get.
am i right? I am still not getting the right answer

Sir_Pogo said:
Are there any hints on this one...I am using Faraday's Law
where EMF = N*(change in flux over change in time). The
magnetic flux is equal to BA, which is the B for the center
of a loop (with radius of the outer circle) times A for the
inner circle...my final equation is coming out something
like this...[(N^2)*Pi*Rb^2*mu*I(nought)*w*cos(w*t)]/(2*Ra)

This is long, but it seems right to me...Any suggestions?
This looks OK, although the answer might be looking for a minus because the emf is the negative of the flux derivative.

Sir_Pogo said:
the velocity induces an emf, the emf gives a current, and
the current gives a backward force F=ILB, so you can set up
and equation mdv/dt=F=-Cv, for some const C you will get.
am i right? I am still not getting the right answer
I assume this was supposed to go with your other problem. It is right if you get C right. So as it asks in the other thread, what function for v will give you a derivative proportional to v?

OlderDan said:
This looks OK, although the answer might be looking for a minus because the emf is the negative of the flux derivative.

I have tried to solved it and got answer in minus more then one time so its might possible. I think you are right...

## 1. How is EMF calculated in metal detector coils?

The EMF (electromotive force) in metal detector coils is calculated using the formula EMF = -NΔΦ/Δt, where N is the number of turns in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time. This formula is based on Faraday's Law of Induction.

## 2. What factors affect the EMF in metal detector coils?

The strength of the magnetic field, the number of turns in the coil, the rate of change of the magnetic field, and the material and shape of the coil all affect the EMF in metal detector coils. Additionally, the presence of conductive materials in the coil's surroundings can also affect the EMF.

## 3. Can the EMF in metal detector coils be measured?

Yes, the EMF in metal detector coils can be measured using a voltmeter. The voltmeter is connected to the ends of the coil, and the change in voltage can be recorded as the coil is moved over a metal object. This change in voltage indicates the presence of a metal object.

## 4. How does the size of the metal object affect the EMF in metal detector coils?

The size of the metal object does not directly affect the EMF in metal detector coils. However, a larger metal object will produce a larger change in magnetic flux, which will result in a higher EMF. This is why metal detectors can detect larger objects at greater depths than smaller objects.

## 5. Are there any limitations to calculating EMF in metal detector coils?

There are a few limitations to calculating EMF in metal detector coils. The calculation assumes that the magnetic field is uniform, which may not always be the case. Additionally, the calculation does not take into account any losses in the coil's resistance or other external factors that may affect the EMF. Overall, while the calculation provides a general understanding of the EMF in metal detector coils, it may not always be entirely accurate.

• Engineering and Comp Sci Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
19
Views
4K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
3K
• Introductory Physics Homework Help
Replies
5
Views
1K
Replies
4
Views
10K
• Introductory Physics Homework Help
Replies
7
Views
5K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
31
Views
4K