Question

Explain the concept of displacement current. An infinitely long perfectly conducting cylindrical wire of radius a is surrounded by a coaxial perfectly conducting cylindrical tube of radius b. The potential difference between the wire and the tube is V(t). Compute V x B in the region between the wire and the tube.

20 Feb 2025
Answer :
Word Count : 575

In classical electrodynamics, the displacement current arises from the time-varying electric field in regions where the electric flux is changing with time. This concept was introduced by James Clerk Maxwell to correct Ampère's law, ensuring its consistency with the continuity equation for charge. Displacement current describes the current associated with the changing electric field, which behaves similarly to the conduction current in circuits. It is mathematically represented as:

\[
I_{\text{displacement}} = \epsilon_0 \frac{\partial \Phi_E}{\partial t}
\]

where \(\epsilon_0\) is the permittivity of free space, and \(\Phi_E\) is the electric flux, defined as the integral of the electric field over a surface.

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