For time varying fields, the electric field is not conservative. Why? Explain with mathematical substantiations.

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter24: Electric Fields
Section24.2: Special Case: Electric Field Of A Charged Sphere
Problem 24.2CE: What is the magnitude of the electric field due to a charged particle at its exact location (r = 0)?
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For time varying fields, the electric field is not conservative. Why? Explain with
mathematical substantiations.

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Step 1

From third Maxwell’s equation, the time-varying electric field is given as,

Physics homework question answer, step 1, image 1

The differential form (by using the stokes theorem) of the above equation can be written as,

Physics homework question answer, step 1, image 2

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