EM Induction:current in one coil inducing current in another

[Taniaz]

Homework Statement

Two coils P and Q are placed close to one another, as shown in the first figure attached. The current in coil P is now varied as shown in the second figure. Show the variation with time of the reading of the voltmeter connected to coil Q for time t = 0 to time t = t 2.

Homework Equations

E = (delta N*flux) / (delta t) and Lenz's law regarding directions.

The Attempt at a Solution

I was trying to make a connection between the gradient of the I vs t graph to the V vs t graph but I didn't quite understand why the gradient of the I vs t graph is the voltage. If this is the case, I get the graph to first be horizontal in the negative region and then there's a spike upwards just before t1 and then a spike downwards towards t1 then it's zero from t1 till t2. The spikes are due to the change in current.

Thank you.

 

[BvU]

Why two spikes ?

 

[Taniaz]

How is it the gradient? It's one spike because of the change in current

 

[cnh1995]

How is it the gradient? It's one spike because of the change in current

Voltage induced in coil Q will be M*di_P/dt, where M is the mutual inductance.
With this equation, will the voltage have a "triangular" spike?

 

[Taniaz]

We haven't taken this equation yet and this is the graph it gives in the mark scheme :/

 

[cnh1995]

We haven't taken this equation yet and this is the graph it gives in the mark scheme :/

This equation is for mutually induced emf. It is actually Faraday's law in disguise(emf =time derivative of flux linkage=constant* time derivative of current that causes the flux).

Take the derivative of current waveform in the given time intervals.

 

[lychette]

Just like the other, similar question you have seen this change in current starts with a steadily, constant rate of increase...you realize what induced emf will be the result (I would call it negative but this is not a big issue)
It looks to me that the next change is very rapid but also constant rate of change giving another emf in the opposite direction (positive in my scheme)
The final current is constant...no rate of change so zero induced emf

 

[Taniaz]

This equation is for mutually induced emf. It is actually Faraday's law in disguise(emf =time derivative of flux linkage=constant* time derivative of current that causes the flux).

I don't understand how Faraday's law is equal to constant* time derivative of current?

 

[cnh1995]

How are flux and current related?

 

[Taniaz]

Mathematically I don't know how but generally speaking if you increase the rate of change of flux, the induced emf and induced current increases

 

[cnh1995]

Mathematically I don't know how but generally speaking if you increase the rate of change of flux, the induced emf and induced current increases

I was asking about the relation between flux linkage of a coil and the current in the coil that causes the flux. (Do not confuse it with "induced" current).

Flux is proportional to current.
Mathematically, Φ∝I and the constant of proportionality is the relevant inductance (self or mutual).

Do you now see how you can write mutually induced emf in coil Q as a function of current in coil P?

 

[Taniaz]

Ah ok, yes that makes sense now. Why does the induced emf graph spike upward when the current spiked upwards?

 

[Taniaz]

Is it because of a sudden decrease in the current?

 

[cnh1995]

Ah ok, yes that makes sense now. Why does the induced emf graph spike upward when the current spiked upwards?

They are considering the effect of minus sign, but it is not compulsory.

Emf is proportional to the "rate of change" of current in P. So you should consider the "slope" of the current waveform (with its sign) at various instants. During the reversal of current, the rate of change is very high (but not infinity). So there will not be a triangular spike as shown in your answer.

 

[Taniaz]

So initally it's just horizontal and at the end it's 0 but what is it in between if it's not a triangular spike?

 

[cnh1995]

So initally it's just horizontal and at the end it's 0 but what is it in between if it's not a triangular spike?

Read #7.

 

[Taniaz]

Oh so it's horizontal and negative for the first bit then horizontal an positive when the current decreases and finally it's horizontal on 0. (Kind of similar to a too hat function?) Will there be vertical lines between the horizontal lines?

 

[cnh1995]

Will there be vertical lines between the horizontal lines?

Yes.

 

[Taniaz]

Thank you :)