# Basic question on induced emf

• bksree
The flux through a superconductor loop is always the same, regardless of the rate of change in flux. This is because the superconductor has zero resistance, meaning the current will flow indefinitely.f

#### bksree

Hi
Please read the attached doc which is excerpted from the text University Physics by Young & Freedman.The discussion is on the emf induced in a loop made of a superconducting material when a magnet is moved towards it.
Doubt 1
It is stated that 'the flux through the loop is exactly the same as it was before the magnet started to move'
Before the magnet moved the flux was downwards and due to the magnet. Once the magnet is moving emf is induced in the coil opposing the motion; so in this case the coil current is CW looking from above and the coil field now opposes the magnet field. Since the coil resistance is zero (superconductor) the current flows even after the magnet is stopped and so the net field after the magnet is stopped is the difference between the downward and upward fields which is NOT the same as the field before motion.

Doubt 2
It is stated that 'so the flux through a loop of zero resistance never changes'
In the above case the flux after motion is the difference between the downward and upward fields which is NOT the same as the field before motion (wherein the flux was downward).

Doubt 3
Is it possible (by adjusting coil radius and magnet motion) to have high current through the wire and net flux (coil flux due to induced current minus magnet flux)upward after motion

TIA

#### Attachments

• Ques1.doc
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You are correct that the induced field in the loop will oppose the field of the magnet. However, you forget to include the fact that the magnet has moved closer to the loop, which means that there is more flux from the magnet contained within the loop (at least if you stop moving it before it passes through the loop). The induced flux will equal the amount of additional flux within the loop from moving the magnet closer. So although the loop field opposes the magnet field, the field within the loop from the magnet becomes stronger as the magnet approaches the loop.

krysith
Thanks for the reply. But my doubts remain :
(1) If the magnet is moved fast and brought to rest (without entering the coil) the rapid change in flux can induce very high current in the coil. Is it possible for this flux to be higher than the initial flux due to the magnet ? (Doubt 3)

(2) Initially the flux through the coil was was downward (due to magnet). After the above magnet motion, there is a running current through the wire (current continues to flow even after magnet is stooped because resistance is zero) and the net flux is the difference between the two fluxes (viz. due to magnet and that due to coil)(doubts 1,2). So the flux through the loop IS NOT EXACTLY THE SAME AS IT WAS BEFORE THE MAGNET STARTED TO MOVE

TIA

I think I understand now why you are having doubts. The infinitely low resistance is throwing off your physical intuition. Remember, you cannot use Ohm's Law to calculate the current in a superconductor. So thinking that a high rate of change of flux means a high induced voltage means a high current is not correct. The superconductor will only generate current to oppose any change in flux, regardless of the rate of change. Think of it like a mirror - it only shows you back what you show it.

Krysith
Thanks.
I wonder what the author means when he says
'Thanks to this persistent current it turns out that the flux through the loop is exactly the same as it was before the magnet started to move, so the flux through a loop of zero resistance never changes. '
and
'Then the induced current will continue to flow even after the induced emf has disappeared - that is, even after the magnet has stopped moving relative to the loop. '

In this case, in what way is the induced emf different in a superconductor vis-a-vis a normal wire ? only in the magnitude of current induced ?

Any explanations ?
TIA