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Are you talking about the famous derivation of the displacement current, where Ampère's law is both true and false depending on what surface you choose to integrate through, despite the same boundary, as below:

http://www.physics.miami.edu/~zuo/class/fall_05/supplement/Figure29_21.jpgCurrent through surfaces S_1 and S_2 are different motivating the introduction of the displacement current

(Image from WikiMedia commons http://commons.wikimedia.org/wiki/File:Displacement_current_in_capacitor.svg)

The solution of this was to add a term to Ampère's equation that depends on the time derivative of the electric field. And then, there is no paradox anymore.

Are you talking about the famous derivation of the displacement current, where Ampère's law is both true and false depending on what surface you choose to integrate through, despite the same boundary, as below:

http://www.physics.miami.edu/~zuo/class/fall_05/supplement/Figure29_21.jpg

The solution of this was to add a term to Ampère's equation that depends on the time derivative of the electric field. And then, there is no paradox anymore.

Are you talking about the famous derivation of the displacement current, where Ampère's law is both true and false depending on what surface you choose to integrate through, despite the same boundary, as below:

Current through surfaces S_1 and S_2 are different motivating the introduction of the displacement current

(Image from WikiMedia commons http://commons.wikimedia.org/wiki/File:Displacement_current_in_capacitor.svg)

The solution of this was to add a term to Ampère's equation that depends on the time derivative of the electric field. And then, there is no paradox anymore.

1
source | link

Are you talking about the famous derivation of the displacement current, where Ampère's law is both true and false depending on what surface you choose to integrate through, despite the same boundary, as below:

http://www.physics.miami.edu/~zuo/class/fall_05/supplement/Figure29_21.jpg

The solution of this was to add a term to Ampère's equation that depends on the time derivative of the electric field. And then, there is no paradox anymore.