Is It Incorrect to Use ∫E . dr in a Moving Conductor?

[Defennder]

There is nothing wrong per se, it's just that in a circuit problem, for example you're usually not given the electric field vector function so you can't use that.

 

[tiny-tim]

And how can we apply Kirchoff's Loop Law in an LR circuit as there is a non conservative electric field induced in the solenoid?
and can anyone please confirm that is emf defined by
∫E . dr
starting from ANY point and ending at the same point on the loop
even in a moving conductor

Kirchoff's voltage law still applies here. Although the electric field is non-conversative, the drop in potential across any circuit loop is still 0 …

Is there anything wrong in using
∫E . dr

Hi anantchowdhary!

Both versions are correct!

The induced emf, from Faraday's Law, is ∫E . dr, and it is measured starting from ANY point and ending at the same point on the loop.

On the other hand, the drop in potential across the loop … between the same two points … is zero.

In the first case, you're only measuring the induced emf.

In the second case, you're measuring the induced emf and the voltage drops.

If the loop is just a wire, with nothing added, then the emf is ∫E . dr, starting from any point and ending at the same point.

But the wire has resistance, so there's an IR to balance it, and that IR is also spread around the whole loop.

Now insert a light bulb, or a voltmeter, anywhere the loop … suddenly 99.999% of the resistance is now in the bulb or voltmeter, so the emf is 99.999% of E . dr, from one end of the bulb to the other.