Why Does a Voltmeter Show a Reading When an Iron Rod is Moved in Coil P?

[Taniaz]

Homework Statement

Two coils P and Q are placed close to one another. P is connected to a power supply whereas Q is only connected to a voltmeter and no supply (see attached diagram). The current in coil P is constant. An iron rod is inserted into coil P.

a) Explain why during the time that the tod is moving, there is a reading on the voltmeter connected to coil Q.

b) The current in coil P is now varied as shown in the figure ( see attached). Show the variation with time of the reading of the voltmeter connected to coil Q from time t=0 to time t=t2.

Homework Equations

Faraday’s law
Lenz’s law

The Attempt at a Solution

I don’t have any issues with part a- the iron rod changes the flux in Q which creates an induced E and an induced I.

In part b, when the current in P in constant, I know the emf induced in Q will be 0. But when the current is intially increasing why is the induced emf constant? And I don’t know what happens when there is a sudden change in the current near t1.

Thank you.

 

[PKM]

In part b, when the current in P in constant, I know the emf induced in Q will be 0. But when the current is intially increasing why is the induced emf constant?

Initially, the current is increasing linearly with time. So the time derivative of the magnetic flux though the solenoid (that's the induced EMF, right?) should be constant.

 

[Taniaz]

Initially, the current is increasing linearly with time. So the time derivative of the magnetic flux though the solenoid (that's the induced EMF, right?) should be constant.

Thank you. What about when it spikes downwards?

Isn’t I/t still a constant so should the graph be something like a top hat function?

 

[PKM]

Isn’t I/t still a constant so should the graph be something like a top hat function?

No, you're missing one point. $I/t$ is still constant, but the slope is -ve. So the induced EMF drops to a negative value as soon as $I$ starts decreasing.

 

[Taniaz]

No, you're missing one point. $I/t$ is still constant, but the slope is -ve. So the induced EMF drops to a negative value as soon as $I$ starts decreasing.

Yes but when the emf drops to the negative value, after that wouldn’t it just stay at that value till the current in coil p becomes constant?

 

[PKM]

Yes but when the emf drops to the negative value, after that wouldn’t it just stay at that value till the current in coil p becomes constant?

Yes, it seems so.
What if we consider the coil P moving toward Q at a steady rate and analyze the case?

 

[Taniaz]

Yes, it seems so.
What if we consider the coil P moving toward Q at a steady rate and analyze the case?

Then I think I/t won’t be constant.
But as for this question it should look like a square wave right? Constant in one direction first, then spikes vertically upwards in the opposite direction and then constant till the current becomes constant?

 

[SammyS]

Homework Statement

Two coils P and Q are placed close to one another. P is connected to a power supply whereas Q is only connected to a voltmeter and no supply (see attached diagram). The current in coil P is constant. An iron rod is inserted into coil P.

a) Explain why during the time that the tod is moving, there is a reading on the voltmeter connected to coil Q.

b) The current in coil P is now varied as shown in the figure ( see attached). Show the variation with time of the reading of the voltmeter connected to coil Q from time t=0 to time t=t2.

Homework Equations

Faraday’s law
Lenz’s law

The Attempt at a Solution

I don’t have any issues with part a- the iron rod changes the flux in Q which creates an induced E and an induced I.

In part b, when the current in P in constant, I know the emf induced in Q will be 0. But when the current is intially increasing why is the induced emf constant? And I don’t know what happens when there is a sudden change in the current near t1.

Thank you.

Please state Faraday's Law.

Is the second graph (Fig. 10.3) your attempt or is it the "correct" answer?

 

[Taniaz]

Please state Faraday's Law.

Is the second graph (Fig. 10.3) your attempt or is it the "correct" answer?

View attachment 237135

I found this graph online somewhere but I don’t think it’s right.