# Homework Help: Electromagnetic Induction

1. Jun 2, 2006

### dannyp

I am a third year aerospace engineering student with very little knowledge of eletricity generation. I currently cannot determine the simple derivation of Faraday's first (i think?) experiment of electromagnetic induciton (bar magnet passing through a loop).

Now i understand that the voltage generated is given by:

V = -N dPhi/dt (change in magnetic flux with respect to time * loops) [i understand that a increase in the velocity through the loop increases the voltage generated]

And i know:

phi = integral of (B * dA) [magnetic flux density by the change in area)

B = mu H (magnetic permeability * magnetic field intensity)

With my formulas aside, I would assume the magnetic field intensity drops off as a function of distance from the loop, but i cannot find any information on this (simple bar magnet i using [does the magnet come with a value of B or H?? these are more questions!]).

As a studying engineer i know all actions have a reaction. There must be a force that will appose the motion of the magnet that induces the electricity. How do i find this force. Is it just F = q u x B ? (charge by velocity cross B [what is q? electron charge? bar magnet charge?])

edit: with more loops would a loop closer to the magnet generate more electricity than one further away? how do i add account for this (i have absoloutely no idea!)? [i think i should get the basics down first!!]

Any information will be fantastic and greatly appreciated. I thank all in advance.

Daniel

P.S. If you're going to help I suppose you'd like to know what it's for! I'm trying to rig up a linear generator (i guess you'd call it?) for an electric hose reel retractor (yes i know i could use a torsion spring, but wheres the fun)

Last edited: Jun 2, 2006
2. Jun 2, 2006

### Hootenanny

Staff Emeritus
Hi Danny,

I think a good resource for you to use, as you seem to have a good grasp of physics would be hyperphysics; http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c1 .

One thing I did notice is you said;

This is not actually the case. The magnetic flux is simply given by the product of flux density and perpendicular area hence; $\phi = BA$

Hope this helps,

~H

3. Jun 2, 2006

### NEWO

the equation F=Bqv is used if a charged particle is moving through a magnetic field. where q is the charge of the particle whether it be an electron, proton, a big ball off iron etc. B is the magnetic flux and v is the velocity of the particle. of course due to B and v being a vector, B is crossed with v. I use F=Bqv because it is easier to rememeber. H is the magnetic field,

4. Jun 2, 2006

### dannyp

thanks for the replies!

Hootenanny:

I had a look at the hyperphysics site, some very useful info there thank you.

As given by the figure in the bottom left of the link you gave me the voltage is proportional of delta B / delta t. Do bar magnets have a constant value of B? What about the space between the magnet and the loops? Does this effect the voltage generated at all?

NEWO:

F=Bqv is for a charged particle moving through a magnetic field. The magnetic field is moving in this case (the bar magnet going through the loop), so would the charged particle just be a single electron inside the loop? all the electrons inside the loop? Very limited understanding on this one.

Thanks for the help so far!

5. Jun 4, 2006

### NEWO

i don't think so, you basically just have an electromagnet, you could apply this if you model the bar magnet is a charged particle which case will not give you an accurate result.

the thing is the loop is also giving off a magnetic field, I don't understand how a magnet can move through a charged coil, because of repulsion, perhaps I'm missing something.

6. Jun 4, 2006

### teken894

I know this forumla:

$$\xi = -N \frac {\Delta \phi}{\Delta t}$$

^^ Faraday's law. It accounts for the number of loops..but for accounting the area of the loop, the flux. phi, depends on area:

$$\phi_{B} = B_{\bot}A = BAcos \theta$$

where A is the area of the coil face.

Hence as the area decreases, the current acts to increase B in the original direction.

7. Jun 13, 2006

### dannyp

NEWO:

the bar magnet is generating current in the loop, its not an electromagnet as i am not applying current to the loop, hope that cleared that up.

I'm still have trouble determining the force acting against the magnet though. I'm not really too concerned about the electricity generated I just want to work out what force will be exerted on the magnet as it moves through the loop generating the electricity. I understand that it's F=Bqv like you said, but does a bar magnet have a constant value of B? Is it different for different materials and/or sizes? What about q? does that depend on the size/material etc? I'm really just don't know!