# Optimum Length & Turns for a Search Coil of a Fluxmeter

## Main Question or Discussion Point

Hello,

I'm investigating the relation of the length and number of turns of a search coil of a fluxmeter (measure magnetic flux). I got to an equation

B= qR/nA

where q is the quantity of charge passed through search coil
R is the combined resistance of search coil and fluxmeter
n is the number of turns of search coil
A is the cross sectional area of search coil

How can I get the optimum length & number of turns for a search coil?

## Answers and Replies

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

berkeman
Mentor
Hello,

I'm investigating the relation of the length and number of turns of a search coil of a fluxmeter (measure magnetic flux). I got to an equation

B= qR/nA

where q is the quantity of charge passed through search coil
R is the combined resistance of search coil and fluxmeter
n is the number of turns of search coil
A is the cross sectional area of search coil

How can I get the optimum length & number of turns for a search coil?
Welcome to the PF.

Can you say more about what you are trying to do? Are you wanting to make a coil sensor for B-field, or a Current Transformer (CT) that senses the current flowing in a wire passing through the coil (a 1:n transformer)? What bandwidth are you hoping to achieve?

Hello berkeman,

I'm sorry for not giving much information. I am trying to make a coil sensor for B-field. I want to find the optimal design of a search coil which will be used to detect and measure magnetic field. The search coil will be connected to a galvanometer which will give readings in either current or flux.

I understand that the higher the number of turns/loops for a coil, the higher its magnetic flux. But I want to find more relation between number of turns/loops, wire length and radius of coil. I'm looking for an optimal design for maximum detection of magnetic flux.

The first part of this article (http://www.solitaryroad.com/c1049.html) shows the relation between magnetic field, resistance and number of turns/loops for search coil. I then assume the resistance of galvanometer is small and the total resistance only dependent on the search coil, hence using relation of

Resistance = Resistivity x Length of wire/Area of wire

Then, I'm stuck. Can anyone shed some light here? A different approach perhaps?

Thanks.

Syed

Mark Harder
Gold Member
Hello berkeman,

I'm sorry for not giving much information. I am trying to make a coil sensor for B-field. I want to find the optimal design of a search coil which will be used to detect and measure magnetic field. The search coil will be connected to a galvanometer which will give readings in either current or flux.
I still don't think you've provided us with enough information to help you. For me, at least, the technical derivation of a constant B field in a simple coil doesn't help at all. So I focus on the quote above... What is moving? A stationary coil in a B-field of constant magnitude and direction will give you nothing. A DC current through a stationary coil likewise produces a stationary B field, and I don't see how that would help you detect a field. Metal detectors employ AC currents in coils to detect metals in their environment. There are many different types, but they all rely on some kind of coupling between the EM generated in the coil and the current in the metal. But that's not magnetic detection or measurement.

I'll hazard a guess that you are describing what's known as a magnetometer. Again, there are different types. Flux gate, atomic magnetic resonance, magnetoresistance and Hall-effect devices are a few. They differ in sensitivity and other features. The least sensitive of these is the Hall-effect device. These are also the cheapest (naturally, the cheapest would be the least sensitive) and are used to detect fields in close proximity, like magnets on moving objects. They can be used on burglar alarms, in which a magnet on a window or door moves toward or away from the detector, or a tachometer that measures the relative velocity of a magnet on a rotating axis. The most sensitive are certain kinds of magnetic resonance detectors, in which the rate at which a proton or other subatomic particles precess around the B field direction can me measured. The measurement is a scalar one - only the strength of the field is measured, not the direction. Portable devices are used in geophysical prospecting for ores, in which case minute variations in the local strengths of the ambient field (i.e. the Earth's mag field and the field it induces in magnetic ore bodies beneath the planet's surface). Flux gate and magnetoresistance detectors are direction sensitive. The latter is used in electronic compasses. You can buy modules that work with microcontrollers from SparkFun and similar hobby electronic suppliers. Flux gate detectors are the only kind that I know use coils. In this case a coil wound on a ferromagnetic core carries alternate current. Because magnetic hysteresis in the ferromagnet is sensitive to asymmetries in the direction of the ambient magnetic field relative to the core, a second coil picks up a current at 2x the input frequency. That makes picking the relatively weak current out of the strong inducing current relatively easy. From the above, you can see how flux gate measurements are vectorial. They have been around since the 1930s and were developed to detect and locate submarines, they are also used in magnetic compasses. There are hobbyists who use them to find antiquities underground. I believe they can also be used in geophysical prospecting, though they are less sensitive than the magnetic resonance types. If you're interested, let me know and I can send you informational links.

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