# Can a straight wire be a self inductor?

1. Aug 17, 2014

### overtak3n

I hope this is posted in the correct thread.
When I was still in my physics class, we learned that a loop of wire with current can act as a self inductor.

Just to refresh my memory:
A loop of wire carrying current has a magnetic field around it due to current, however if the current changes, the magnetic field changes. This change in magnetic field makes the wire induce a current in the direction such that it opposes the change in magnetic field. Thus the induced current is in the direction opposite of the direction of the change in current.
Thus a loop of wire is a self-inductor since it does not require any external magnetic field to induce a current, it just requires a change in current which causes a change in magnetic field.

1) Is this correct? Please correct me if I am wrong anywhere, since I'm just refreshing my memory.

2) My question: While a loop of wire can be a self-inductor, can a straight wire also be a self-inductor?

3) Another question: I also learned current can be induced if there is a magnetic field and a loop of wire rotates, or its area changes. In addition, current is induced if the magnetic field changes.
By "magnetic field changes" does that mean the strength of the magnetic field changes?

Hopefully this can be answered in simple terms.

Thanks.

Last edited: Aug 17, 2014
2. Aug 17, 2014

### Simon Bridge

Inductance happens when there are charges in a changing magnetic field.
If a wire loops back on itself, and it has a current, then part of the wire is in the magnetic field of another part of the wire. This does not happen for straight wires.

... it means the magnetic flux changes... this usually means the magnetic field changes.

When you are first introduced the electricity and magnetism, it is taught as a collection of separate formulae and phenomena. As you advance, the different ideas get unified. To get a more complete picture, look at Maxwell's equations.

3. Aug 17, 2014

### overtak3n

Thank you for the response.

That makes sense. In a loop of wire, for example, the opposite side of the wire of one part would create what would be like an external magnetic field to that part of wire. That's how I understand your explanation.

To your response with regard to changing magnetic field: This leads me to another question: Will changing the strength of the magnetic field induce current?

4. Aug 17, 2014

### Meir Achuz

"2) My question: While a loop of wire can be a self-inductor, can a straight wire also be a self-inductor?"
A straight wire does have self inductance.

5. Aug 17, 2014

### overtak3n

Thank you. Seems to contradict what Simon said. Hmm which answer is correct?

6. Aug 17, 2014

### Simon Bridge

I don't think it is contradictory - I just left out a situation ;)
Meir's answer is part of that "more complete picture" that I mentioned at the end of my reply.

What education level do you need the answers for?

7. Aug 17, 2014

### Simon Bridge

Yes - this is how generators work.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

A time-varying magnetic field produces an electric field.
A time varying electric field produces a magnetic field.

8. Aug 17, 2014

### Baluncore

The self inductance of a straight wire of length s and diameter d in mm, is LuF = 0.2 * s * ( Loge( 4 * s / d ) – ¾ )

9. Aug 17, 2014

### overtak3n

So a changing magnetic field doesn't necessarily mean changing magnetic flux, it could mean changing magnetic field strength? Are those the same thing, no?

By time varying electric field, are you referring to current?

As for which education level, college but I just wanted simple answers that answer the question

10. Aug 18, 2014

### Simon Bridge

1. What is the definition of a magnetic field.
2. No. A time varying electric may exist in a region of space where there are no charges.
3. What counts as simple depends on the education level ;) Have you had a look at Maxwells eqs yet?

11. Aug 18, 2014

### overtak3n

1. Space around which there exists a magnetic force (I'm assuming it can vary in strength too)
3. Yep.

12. Aug 19, 2014

### Simon Bridge

1. Erm OK for now, consider: "What is the definition of magnetic flux?"
3. In maxwell's equatons, the symbol "j" is the current density. You'll see equations with thatn in it, as well as time varying E and B.
2. In maxwel, $\rho$ is the charge density - you can still get sensible solutions for $\rho=0$.

The easiest form to see the relations and appreciate how they hang together is the differential form.

13. Aug 19, 2014

### overtak3n

1. I think it's the magnetic field passing through a surface.

Thank you for helping. The physics course I took only required integral calculus. I still need to complete my math courses before I fully understand differential equations

14. Aug 19, 2014

### Simon Bridge

So you can see that magnetic field and magnetic flux are related.
Do you know the mathematical relation that links them?
... once you have that, you should be able to answer your own question ;)
http://en.wikipedia.org/wiki/Magnetic_flux

You should still be able to read the differential form ... where $\Delta x$ is a change in x, and $\delta x$ is a small change in x, you read the "dx" notation to be an extremely small change in x. i.e. acceleration is the rate if change of velocity ... which is written: $$\vec a =\frac{d\vec v}{dt}$$ ... the integral form would be $$\vec v = \int \vec a(t) \; dt$$ ... you should be able to get the idea by replacing the d's with deltas.

In Maxwell's equations the symbol $\nabla$ is used a lot - that just denotes a change in the variable with an extremely small change in space.

But you will need to complete your math courses to have a chance to understand some of the connections between electricity and magnetism yeah.

15. Aug 19, 2014

### overtak3n

Thank you Simon.

Is the symbol ∇ used in Maxwell's equations the same as the symbol ∇ used in calculus for gradient?

16. Aug 21, 2014

### Simon Bridge

Pretty much. In Cartesian coordinates: $$\vec \nabla = \begin{pmatrix}\frac{\partial}{\partial x}\\ \frac{\partial}{\partial y}\\ \frac{\partial}{\partial z} \end{pmatrix}$$... which allows it to be used with dot and cross products on vector functions. Recall $\vec E = E_x(x,y,z)\hat\imath + E_y(x,y,z)\hat\jmath + E_z(x,y,z)\hat k$ ... which is kinda difficult to use the grad operation on.
See: http://en.wikipedia.org/wiki/Del