Wire cutting magnetic field lines

[Entanglement]

emf is defined as work done per unit charge on a charge moving round a circuit.
If charge q moves through length L of conductor, work done on it will be force x distance = BqvL

So emf = work done per unit charge = BqvL/q = BLv.
I'm assuming for simplicity that the wire is at right angles to its direction of motion.

So the emf in the Ariel (Bvql/q) is calculated by the same law of a wire widening and narrowing a loop ( B delta A = Blv ) so that's just a coincidence?

 

[Philip Wood]

No, it's not a co-incidence! I've taken the view throughout this thread, that emf is only correctly spoken about for a closed loop. If the whole of the loop moves with the aerial (top digram) there is no emf in the loop. If the rest of the loop is stationary (bottom diagram) there is an emf, BLv, which can correctly be written as B delta A/Delta t, in which A is the loop area.

Please ignore this post. It is replaced by a post with thumbnail.

 

[Entanglement]

No, it's not a co-incidence! I've taken the view throughout this thread, that emf is only correctly spoken about for a closed loop. If the whole of the loop moves with the aerial (top digram) there is no emf in the loop. If the rest of the loop is stationary (bottom diagram) there is an emf, BLv, which can correctly be written as B delta A/Delta t, in which A is the loop area.

I understand the moving loop as all or just a part of it, thanks to you in the earlier posts of this thread But in the case of the an actual aerial there's no loop so we calculate the emf from Blv which is derived from Bvql and not B delta A / delta t ?

 

[Philip Wood]

No, it's not a co-incidence! I've taken the view throughout this thread, that emf is only correctly spoken about for a closed loop. If the whole of the loop moves with the aerial (top digram) there is no emf in the loop. If the rest of the loop is stationary (bottom diagram) there is an emf, BLv, which can correctly be written as B delta A/Delta t, in which A is the loop area.

 

[Philip Wood]

But in the case of the aerial there's no loop yet we calculate the emf from Blv which is derived from Bvql and not B delta A / delta t indeed

We've been here before! My view is that strictly it's wrong to talk about the emf in the aerial. It's only correct to talk about the emf in a complete loop. You have to make the aerial part of a loop. Then it does make sense to talk about the loop area changing.

If you choose a loop ALL of which moves with the car (see my top diagram in post 74) there is no emf, and there is no rate of change of loop area, so we have consistency.

[But as discussed earlier, rate of change of loop area is hard or impossible to apply in the case of the clock-hand, even when the hand is included in a suitable circuit.]

 

[Entanglement]

We've been here before! My view is that strictly it's wrong to talk about the emf in the aerial. It's only correct to talk about the emf in a complete loop. You have to make the aerial part of a loop. Then it does make sense to talk about the loop area changing.

So practically speaking No loop -------> no emf ??

But I'm not talking about a changing area I'm talking about the emf induced due to "Lorentz force" even if the loop doesn't exist as I understand from the earlier posts

 

[Philip Wood]

I do understand where you're coming from here. You can indeed calculate the work done per unit charge on the moving charges in the aerial. It is BLv. And this would be measured in volts, like emf. I'd call it a CONTRIBUTION to the emf. That's because I think emf should only be applied to the complete amount of work done per unit charge on a charge going round a complete circuit. If you stick to this idea of emf, then BLv DOES equal B times dA/dt, i.e. rate of change of flux linking the circuit.

If, loosely, you talk about BLv as the emf in just the aerial, then, as you say, rate of change of flux doesn't make sense. My recommendation is to be rigorous and only talk about emfs in complete circuits. If there is no obvious circuit - imagine one! That will also help you to understand how you could MEASURE the emf.

 

[Entanglement]

I do understand where you're coming from here. You can indeed calculate the work done per unit charge on the moving charges in the aerial. It is BLv. And this would be measured in volts, like emf. I'd call it a CONTRIBUTION to the emf. That's because I think emf should only be applied to the complete amount of work done per unit charge on a charge going round a complete circuit. If you stick to this idea of emf, then BLv DOES equal B times dA/dt, i.e. rate of change of flux linking the circuit.
If, loosely, you talk about BLv as the emf in just the aerial, then, as you say, rate of change of flux doesn't make sense. My recommendation is to be rigorous and only talk about emfs in complete circuits. If there is no obvious circuit - imagine one! That will also help you to understand how you could MEASURE the emf.

So in the case of just an aerial there is an emf due to Lorentz force calculated from blv but we shouldn't talk about an emf here because there is no practical circuit and the emf should be the total work done on a coulomb through a full cycle in the loop. Isn't that correct ?

 

[Philip Wood]

Yes, that's my view. I'd be happy about calling BLv a contribution to the circuit emf. And I have to admit that most people probably refer to BLv as the emf in the aerial. This is fine as long as it's understood to be shorthand for the contribution that the aerial would make to the emf in a circuit of which it forms part!

 

[tiny-tim]

Hi Philip! Hi ElmorshedyDr!

So practically speaking No loop -------> no emf ??

You can indeed calculate the work done per unit charge on the moving charges in the aerial. It is BLv. And this would be measured in volts, like emf. I'd call it a CONTRIBUTION to the emf.

That's because I think emf should only be applied to the complete amount of work done per unit charge on a charge going round a complete circuit. If you stick to this idea of emf, then BLv DOES equal B times dA/dt, i.e. rate of change of flux linking the circuit.

If, loosely, you talk about BLv as the emf in just the aerial, then, as you say, rate of change of flux doesn't make sense. My recommendation is to be rigorous and only talk about emfs in complete circuits …

So in the case of just an aerial … we shouldn't talk about an emf here because there is no practical circuit and the emf should be the total work done on a coulomb through a full cycle in the loop. Isn't that correct ?

Yes, that's my view. I'd be happy about calling BLv a contribution to the circuit emf.
And I have to admit that most people probably refer to BLv as the emf in the aerial.
This is fine as long as it's understood to be shorthand for the contribution that the aerial would make to the emf in a circuit of which it forms part!

personally, i think of Blv as representing an imaginary battery in the aerial, and i see nothing wrong with calling the work done by moving 1 C along the aerial "the emf induced in the aerial"

an actual battery in the aerial would produce no current (since there's no circuit)

if you complete the loop with a moving circuit (Philip's first diagram), then there's an identical imaginary battery on the other vertical side of the loop: the two batteries cancel, so the emf (of the whole circuit) is 0

if you complete the loop with a circuit with one end fixed (Philip's second diagram), then there's only one imaginary battery, and the emf (of the whole circuit) is equal to the voltage of that imaginary battery, Blv

does the imaginary battery create a voltage difference in the same way as a real battery does?

no

voltage difference is a difference in potential energy, and potential energy is defined as (minus) the work done by a conservative force … but (although the electric field of a battery is conservative) the electric field "induced" by a changing magnetic field is not conservative

this is not mere semantics … the voltage difference from point A to point B (like gravitational potential difference) should not depend on the path taken

in a real battery circuit, it doesn't: going all the way round the circuit takes you through the battery, which cancels out the gain you made from the battery: the work done going either clockwise or anti-clockwise is 0, and the voltage difference from point A to point B (as in gravity) is unambiguous

but in a imaginary battery circuit (ie in an https://www.physicsforums.com/library.php?do=view_item&itemid=294flux-induced circuit), nothing cancels as you go all the way round: the work done going clockwise is minus the work done going anti-clockwise, and both are non-zero … and so the work done from point A to point B clockwise is ambiguous: in other words, it (and the voltage) cannot be defined

this inability to define a voltage in a flux-induced circuit requires a new concept, called emf, defined of course as the work done on 1 C around the circuit in a particular direction

(see also http://en.wikipedia.org/wiki/Electromotive_force#Electromotive_force_and_voltage_difference)

example: suppose we have three vertical aerials, joined by two horizontal wires at top and bottom: so we have one outer loop and two inner loops

suppose the magnetic field is not uniform, so that dflux/dt = emf through the outer loop is 6V, and through the inner loops are 2V and 4V (all the same way): then my imaginary batteries would be 7V 5V and 1V (all the same way)

if they were real batteries, and if the three parts of the circuit each have resistance 1Ω, then the currents upward through the three batteries would be 8/3 A, 2/3 A, and -10/3 A

the result for the flux-induced set-up is the same

it seems to me far easier to work this out by finding the imaginary batteries first, ie what we're not supposed to call "the emf induced in the aerials"!

 

[Philip Wood]

tiny-tim: I see exactly where you're coming from. My wish to cling on to emf as a whole-loop line integral is partly motivated by my wish to use Faraday's law in the form emf = rate of change of flux linkage, which then neatly works for either moving circuit boundaries or changing flux densities: one equation applying to two phenomena. Without a circuit we can't do this (one of ElmorshedyDr's concerns). We can, of course, still talk about rate of flux CUTTING, but that doesn't have the same uniting quality.

Another thing I like about insisting on a complete circuit is that it forces one to think about how you'd MEASURE the induced voltage; for example a voltmeter moving with the car and connected across the aerial would give zero. [I'm not advancing this as a major argument for showing that emf can only be applied to a complete loop.]

 

[kira506]

ElmorshedyDr. Yes. If the aerial is vertical but it's moving horizontally, $\mbox{sin}\ \theta$ will be 1 in our previous discussion.

kira506. Bqv is the force on a charge q moving at speed v at right angles to a magnetic field B.

emf is defined as work done per unit charge on a charge moving round a circuit.

If charge q moves through length L of conductor, work done on it will be force x distance = BqvL
So emf = work done per unit charge = BqvL/q = BLv.

I'm assuming for simplicity that the wire is at right angles to its direction of motion.

sometimes is inclined by angle theta but in most cases it is perpendicular to field and direction of motion
thanks , that was really helpful , thanks to your awesome explanation .I now know how this rule was derived,you should consider being a physics teacher (that's if you're not already one c: )