# Increase emf received from a coil without changing flux source

I have a situation where I'm trying to increase the amount of power received by a coil. To my understanding, I can increase the emf (voltage) by doing one of 4 things:

1. Increase the number of coils ($$\ N \$$)
2. Increase the field from the source by increase the current ($$\B\$$)
3. Increase the area of the coil ($$\A\$$)
4. Decrease the time it takes to change field ($$\t\$$)

Which is coming from the following equations below:

emf Equation: $$\epsilon = -N\frac{\Delta \Phi}{\Delta t}$$ where $$\Phi=BAcos(\theta)$$

$$\A\$$ is the area of the coil, and $$\B\$$ is the flux given by $$B=\frac{\mu_0 I}{2\pi r}$$

so without chaning anything about the source of the field, the only way i can increase the emf of the coil is to change the number of coils, or change the area, right?

let's say my coil is a wrapping around the source of the field, with the source of the field running through the middle as shown below, and the coil is a square coil with equal height and width.

I'm wanting to know if I can do one of the following to increase the emf.

1) can I simply increase the area of the coil by increasing the height as shown below (note, i might do this if my width is limited but my height isn't)? I'm not sure if this will have any negative effects since it's not as uniform in all directions, and if there are negative effects, how big of a deal they are.

2) can i keep my square coil roughly the same shape width and height wise, but then wrap the that around my source in a helix form. if i wrapped my wire around a long thin rod, and then wrapped that rod around my source, I'd get something like below. My thought is that i would increase my area, and the number of turns, and that it might easier to make then simply increasing the height as seen in the previous diagram.

I feel like this helix method will have some downsides. I'm thinking that the field created by the coil with be fighting itself, thus reducing the over all emf... maybe this can be reduced by stretching the helix out... but by doing that i'll be increasing my $$\\theta \$$, which will reduce my $$\ \Phi = BA cos(\theta) \$$... maybe the increase in coils or area will overcome this decrease from the angle... I'm not sure. Is a helix coil even done?

I feel like could acheive the same thing with multiple coils in series like the diagram below. I think I would run into the the same issue of my fields fighting against each other, but my $$\theta \$$ would still be zero, so i wouldn't be losing any energy from my angle.

Do any of these methods sound like a valid way of increasing my emf? are they're better/easier ways of doing this apart from just increasing the number of turns in my coil, or increasing my coil in both width and height? Thanks for any feedback!

• None of your diagrams shown will produce any induced voltage in the receive coils. You need to read up on how induction works. Basically you have your coils wrapped around a conducting wire and this just doesn't work at all. – Andy aka Jul 23 '19 at 7:18
• @immibis, yeah I was thnking the increase in angle would decrease the over all effective area... just wasn't sure if it would have some overall increase in area. Do you think the multiple coils approach would practically work though? I'm thinking they would fight against each other with the field that the coils create... but if i spaced them far enough apart, the field should be weaker and so shouldn't have as much of a negative effect. – gerrgheiser Jul 23 '19 at 13:33
• @Andyaka, My coils are perpendicular to the conducting wire. what i was trying to show was having my conducting wire in the center, and then the wires wrapped around ring on the outside, similar to how a toroid is wrapped (so going up, right, down, left, rather than just wrapping the wire around a spool). The first picture that voltage-spike posted is what i was trying to represent. – gerrgheiser Jul 23 '19 at 13:39
• You need to make an attempt to show the coils directions then because at the moment your diagrams are at best ambiguous. – Andy aka Jul 23 '19 at 13:57

Look at current transformers:

Source:

https://www.electronics-tutorials.ws/transformer/current-transformer.html

Remember that the magnetic field of a wire flows with the right hand rule with the magnetic field flowing in a circle around the wire:

Building a coil directly around a wire like the helix method will have some downsides, the magnetic field lines running through the coil will be perpendicular to the coil. In other words the coil won't pick up much magnetic field and the current will be close to zero.

So build a coil perpendicular to the field lines, like the current transformer.

• Right! that was my thinking do about being perpendicular to the field. If i'm trying to increase my current though, are their downsides to increasing the height of my of my secondary coil without increasing the width as much? so that my secondary coil would essentially look like a long tube with the primary conductor running through the middle? Also, what about having multiple smaller coils stacked up and connected in series? Am i correct in thinking that these coils would fight against each other a bit? Thanks for your feedback! – gerrgheiser Jul 22 '19 at 22:00
• There is more field closer to the wire and it falls with 1/r. Ideally you'd want a flat coil closer to the wire. – Voltage Spike Jul 22 '19 at 22:05