Explaining Induced Voltage: -NBA/t

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SUMMARY

The discussion centers on the calculation of induced voltage using the formula Induced Voltage = -NBA/t, where N represents the number of turns in the coil, B is the magnetic field strength in Tesla, A is the area of the coil in square meters, and t is the time in seconds. Participants clarify the significance of the negative sign, which is explained by Lenz's Law, indicating the direction of induced current opposes the change in magnetic flux. The conversation also touches on the importance of understanding the geometry of the coil and the rate of change of magnetic flux for accurate voltage calculations.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Knowledge of Lenz's Law and its implications
  • Familiarity with basic geometry for calculating the area of a coil
  • Concept of magnetic flux and its units (Tesla, Gauss)
NEXT STEPS
  • Study the derivation and applications of Faraday's Law in different scenarios
  • Learn how to calculate the area of various coil shapes, including circular and rectangular coils
  • Explore the relationship between magnetic field strength and induced voltage in practical applications
  • Investigate the effects of coil rotation speed on induced voltage and current generation
USEFUL FOR

Students, electrical engineers, and hobbyists interested in electromagnetism, particularly those working on projects involving electromagnetic induction and current generation.

bigmack
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Induced Voltage = -NBA/t
I know the equation, but could someone please explain it to me?
 
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Try this: http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/farlaw.html"
 
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hmm that looks good, but how do you get "A" ?
oh and why is there a negative sign?
 
bigmack said:
hmm that looks good, but how do you get "A" ?
"A" is the area of the coil.
oh and why is there a negative sign?
Read about Lenz's law at the bottom of that same page.
 
ok. but how do you find the area of the coil?
 
bigmack said:
but how do you find the area of the coil?
Using a bit of geometry. For a circular coil, the area is \pi r^2.
 
ok so wait, does the radius of the coil include the diameter of the wiring?
or is it just the area within the coil, and not including the wire
 
Measure the radius to the center of the wire. (For thin enough wires, it won't matter.)
 
oh ok.

so let's just see if i get it.
to calculate the induced voltage, you check the area of the field, you multiply it with the strength of the magnet, divide by the speed of the wire and multiply by the number of turns of the wire.

wait, what are the units?
B is in Tesla, right? but what about A and t ?
 
  • #10
bigmack said:
to calculate the induced voltage, you check the area of the field, you multiply it with the strength of the magnet, divide by the speed of the wire and multiply by the number of turns of the wire.
What you really want is: Induced Voltage = -N Δ(BA)/Δt, where Δ(BA)/Δt is the rate of change of the magnetic flux (BA). (Read the explanation on the website I linked.)
wait, what are the units?
B is in Tesla, right? but what about A and t ?
Yes, the magnetic field has units of Tesla. Area has units of meters²; time has units of seconds.
 
  • #11
bigmack said:
Induced Voltage = -NBA/t
I know the equation, but could someone please explain it to me?

I'm not sure I understand the question. The induced emf on a coil of wire depends on the wire's shape, the rotation speed, the time dependence of the magnetic fields, and other specifics of the problem. The usual example is a coil of circular wire spinning in a constant magnetic field, in which case the induced voltage is,

emf = \omega NBA cos\left(\omega t\right)

The equation you gave says that the induced emf will decay over time, tending to zero. What's the physical situation here?
 
  • #12
Doc Al said:
What you really want is: Induced Voltage = -N Δ(BA)/Δt, where Δ(BA)/Δt is the rate of change of the magnetic flux (BA). (Read the explanation on the website I linked.)

Yes, the magnetic field has units of Tesla. Area has units of meters²; time has units of seconds.

Ok thanks, you've been a lot of help.

arunma said:
I'm not sure I understand the question. The induced emf on a coil of wire depends on the wire's shape, the rotation speed, the time dependence of the magnetic fields, and other specifics of the problem. The usual example is a coil of circular wire spinning in a constant magnetic field, in which case the induced voltage is,

emf = \omega NBA cos\left(\omega t\right)

The equation you gave says that the induced emf will decay over time, tending to zero. What's the physical situation here?

Its the upper right picture in Doc Al's link, the one in which you move a magnet in a coil
 
  • #13
wait no that's not what i meant.

im confused. what you're saying has a magnet cut the field lines. what i was thinking was the field lines could be cut by the coil, is that possible?

i mean can i place two magnets side by side, and drop a coil of wire in between them to induce voltage?
 
  • #14
Help with Gauss

To calculate the voltage induced when cutting magnetic field lines you need to know the strength of the magnets in Gauss.

I was looking at some magnets I would like to buy for a project.
The magnets had 2 different values for the gauss.

"Brmax (Residual Induction) or Residual Flux Density "

and

"Surface Field (Surface Gauss)"

which reading is used to calculate the voltage induced?
 
  • #15
Is there a specific problem you are trying to understand?

That formula you started the thread with is a simplified form of Faraday's law, as I tried to explain. A more useful form is what I gave in post #10 (and is described in the link). But that version is also limited to certain situations--a more complicated situation (where the coil rotates, for example) requires a different version of Faraday's law.

What are you trying to do?
 
  • #16
ok.
im trying to generate current by cutting magnetic fields with wiring coiled around an iron core.

all i want to know is how much current I am going to get and the voltage too.
 
  • #17
if you can help some more id really appreciate it
 
  • #18
bigmack said:
ok.
im trying to generate current by cutting magnetic fields with wiring coiled around an iron core.

all i want to know is how much current I am going to get and the voltage too.
That's not a simple problem. You need to know the rate at which the magnetic flux through your coil is changing at any given time. That will allow you to find the induced voltage at that moment using Faraday's law.
 
  • #19
so how would i do that?
the speed at which the coil cuts fields?
can you like just give me a worked out example, using whatever numbers you want.
 
  • #20
hello??
 

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