Wire moving at constant speed in a magnetic field

[elemis]

So let's say I have a wire of length l moving in a uniform magnetic field of constant velocity.

Now the induced EMF = Blv

Constant velocity implies constant EMF generated per unit time.

I even have a graph of EMF vs time in my textbook for such a situation showing a flat horizontal line for the induced EMF.

My question is how can this be true ?

The wire cuts the same number of magnetic field lines per unit time. Hence, isn't the rate of change of magnetic flux linkage zero ?

So what would a graph of EMF vs time look like for the above situation ?

 

[Emilyjoint]

Ah no...we have done this question...the rate of change of flux linkage is CONSTANT...that does not mean it is zero.
The emf is constant like you said

 

[tiny-tim]

hi elemis!

So let's say I have a wire of length l moving in a uniform magnetic field of constant velocity.

Now the induced EMF = Blv

Constant velocity implies constant EMF generated per unit time.

I even have a graph of EMF vs time in my textbook for such a situation showing a flat horizontal line for the induced EMF.

My question is how can this be true ?

The wire cuts the same number of magnetic field lines per unit time. Hence, isn't the rate of change of magnetic flux linkage zero ?

ah, what flux? it's just a straight wire!

you need an area for flux … if this wire was joined by perpendicular wires to a circuit which completed outside the magnetic field, then the flux would increase at rate Blv

but if the whole circuit is inside the field, the flux is constant

yes the emf along the wire is Blv, but if you complete the circuit, that emf may or may not be canceled by an opposing emf at the opposite side of the circuit ​

 

[Bob S]

This principle can be made into a dc current generator called a Faraday disk or a homopolar generator. A large (500 megajoule) homopolar generator (with stationary magnet and rotating disk) was built and used at ANU (Australian National Univ.) for several years. See http://en.wikipedia.org/wiki/Homopolar_generator

 

[Emilyjoint]

the example we did was a wire moving at right angles to a uniform magnetic field. An area (=lxv) was swept out each second.
We use this to calculate the voltage developed across the ends of an aeroplane wing flying through the Earth's's field

 

[elemis]

hi elemis!


ah, what flux? it's just a straight wire!

you need an area for flux … if this wire was joined by perpendicular wires to a circuit which completed outside the magnetic field, then the flux would increase at rate Blv

but if the whole circuit is inside the field, the flux is constant

yes the emf along the wire is Blv, but if you complete the circuit, that emf may or may not be canceled by an opposing emf at the opposite side of the circuit ​

Could you check the following ?

A wire which is connected in no way to anything else will induce a constant EMF across itself if it cuts a magnetic field at constant speed ? If it is accelerating the graph of EMF vs time would be a straight line of constant gradient through the origin ?

This because as per Fleming's Right Hand Rule electrons in the wire feel a magnetic force (consider the magnetic field is into the page) that directs them towards the bottom of the wire. Thus, an EMF is generated across the wire.

Would there be a circular flow of eddy currents in the wire ?

 

[Hassan2]

The wire cuts the same number of magnetic field lines per unit time. Hence, isn't the rate of change of magnetic flux linkage zero ?

So what would a graph of EMF vs time look like for the above situation ?

This is a case of " motional emf" and should be analyzed using the corresponding equations. However if you want to interpret it as a case of Faraday's law, then consider the wire to be a part of a closed loop where the rest of the loop stays outside the field. Now as the wire moves forward/backward, more lines enter/exit the loop, increasing/decreasing the flux linkage.

 

[elemis]

This is a case of " motional emf" and should be analyzed using the corresponding equations. However if you want to interpret it as a case of Faraday's law, then consider the wire to be a part of a closed loop where the rest of the loop stays outside the field. Now as the wire moves forward/backward, more lines enter/exit the loop, increasing/decreasing the flux linkage.

Ah, that is quite a nice analogy... Thanks ! :)

 

[tiny-tim]

A wire which is connected in no way to anything else will induce a constant EMF across itself if it cuts a magnetic field at constant speed ? If it is accelerating the graph of EMF vs time would be a straight line of constant gradient through the origin ?

This because as per Fleming's Right Hand Rule electrons in the wire feel a magnetic force (consider the magnetic field is into the page) that directs them towards the bottom of the wire. Thus, an EMF is generated across the wire.

yes …

the electrons feel a (magnetic) force along the wire, which we interpret as an voltage difference (an emf)

flux has nothing to do with it, though you can introduce a "pretend" flux to get the same result!

as Hassan2 says, you should use the equations appropriate for the problem, rather than try to make similar equations fit

Would there be a circular flow of eddy currents in the wire ?

no