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enter image description here

Considering this question, i think the concept used is wrong coz direction of E produced due to changing magnetic field is along the circular loop(tangential at each point on loop) of radius r. While if we use the formula for displacement current $$i_d= \epsilon_0 \frac{d\phi_E}{dt}$$ where $\phi_E$ should be electric flux through circle of radius r, but since E produced is along loop and perpendicular to the area vector of circle of radius r thus $\phi_E$ should be 0.

So, is the solution wrong?

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  • $\begingroup$ People, the problem is in concept of the question, i am not asking to solve this question, please consider before downvoting. $\endgroup$
    – SHINU_MADE
    Commented Apr 1 at 15:04
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    $\begingroup$ Pictures of problems are discouraged here, instead type out the important conceptual parts of the problem using MathJaX. You also provided no real work showing how you somehow reached a different answer using that equation. I can tell you right now it's probably because you used the wrong gaussian surface. $\endgroup$
    – Triatticus
    Commented Apr 1 at 15:22
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    $\begingroup$ The question Q60 is using inaccurate terminology - they ask about displacement current, but then they answer as if the question was about displacement current density $\frac{\partial \epsilon_0 \mathbf E}{\partial t}$. The latter has definite direction and value at any point of space, thus they really wanted to ask about displacement current density, not displacement current. Displacement current you refer to depends on the surface chosen, and if you choose the circular disk in the plane of the coils for that, then the displacement current is zero. $\endgroup$
    – Ján Lalinský
    Commented Apr 1 at 20:29
  • $\begingroup$ @JánLalinský I am very thankful to you replying to the follow up question, your comment-cum-answer has indeed cleared all my doubts. $\endgroup$
    – SHINU_MADE
    Commented Apr 2 at 4:28

1 Answer 1

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For an infinitely long cylinder the current can be decomposed into a circular and an axial current. A purely circular current can be accomplished by a wire in two layers winding helix up and down. Then one has

$$\vec B(t) = B(t) \vec e_z $$ inside and B=0 outside such that by definition

$$J = \nabla_{r,\phi ,z} \times B(t) \Theta (R-r) \vec e_z =B(t) \delta (R-r) \ \vec e_{\phi}$$

This is Stokes and Maxwells definition of the curl as the limit of a line integral over a small flat rectangle inside and outside.

The flat box integrals over a conducting surface to determine charge and current by Gauss and Stokes theorems was the classical tool for experimental physicists as one finds the demonstrations in the old classical texts on electrodynamics.

The electric field induced is confined to the inner of the coil, too, where it may act on an inner coil as a transformer.

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